Nice piece! I do have some points:
2nd line 'See' I don't know why you start it with capital letter.
3rd line 'Glow' again with capital.
4th line 'Grassy', 'Yellow' and 'Light' again with capital letter.
'Attract' I guess should be 'attracting' and 'rewrite' maybe 'rewritten' or 'to rewrite'.
'whose' maybe you mean "who's"
'covering' should be 'covered' and 'spend' should be 'spending'

The whole poem needs some repairing in my opinion.
Good attempt.

I think the contents of the poem is sad and good, so well done:)

A very thoughtful write... I found it very sad and gloomy...
Good work:)

This poem is mysteriously sad. I think the man is a killer or he pleasures by hurting others. What is his motive? What justification does he has for his actions? Is he having any abnormality or does he has any history of pshyce problem? Its a deep piece, seem like a scene in a thriller movie. You can broaden it a bit, so we know his plot. I like how you progressed in telling this mans story. Its gets one eager to get to the other line, anticipating randomly. A good theme, keep it up!. Meri hindi tora tora hai. ;) ..

Firs of all: WOW! on the title. It's long but totally attention grabbing. Love it.

The bench underneath the lamp on the footpath
^^
A little advice I myself have been given in the past - avoid using the title as the first line of the poem - I think it ruins the suspense or something, perhaps other reasons also. Just something I thought to share.

As I See from my room window in cold night
^^
'See' is unnecessarily capitalised I believe ..?

The place Glows and Looks like a shower light bath
^^
not sure 'bath' belongs here.. but it's your poem and you'd know the meaning more than I would. haha. Also the capitalisation of 'glows' and 'looks' seems unnecessary to me.

where Grassy bloom and the park just at other side
^^
Again 'grassy' seems unnecessarily captalised. Also I think the end of this line should read like: 'at THE other side' instead.

Makes me feel the lonely place of silence
^^
Love this line and it is relatable to many. But I think silence doesn't nessarily have to mean loneliness but rather peacefulness. I like your arrangement and word choice here.

Nearby the bunch of houses are very quiet
^^
This line really sets the scene and kind of the mood too. It's simple yet desciptive - it just goes to show that writers don't need immense detail in order to create a good description. Sometimes less is more.

Yellow dim Light on the surface with its wetness
^^
'Light' -- don't believe this needs capitalisation, but this could be an exception because it can be somewhat personified whereas the other words above cannot be. I like the contrast between light and wetness - - the metaphor you have used. Really unique.

Attracts me again to sit there to something rewrite
^^
Consider rephrasing this line. Perhaps it could read: 'to ponder a rewrite' -- that way it doesn't mess with your rhyming yet allows the line to make more sense.

I wonder whose turn to sit there in this cold night!
The invitation from the lamp on the lonely place
Somebody sits there when nothing happens alright
The Place when nothing left behind anything to chase
^^ Consider rephrasing this last line. The ending doesn't quite make sense -- it's the word 'anything' I think.

Finally the man covering with black jacket appears there
^^
'covering' should be 'covered' I think

For spend the night on the bench under the street light
^^
'spend' should be 'spending'

I hope and wish for him to be everything well and fair
Though nothing new for me, it happens in several nights.
^^
I like this ending, it's satisfactory in that it ties things up - but I feel like it lacks somehow. Like it doesn't really make a BANG! like it should. It doesn't make a statement which many do. Maybe that's your personal style of writing, I don't know.

Overall;
Okay, I've been highly critical above. SORRY! But I really do hope my critiques offer some help, as it only needs some minor tweaking. I can honestly see it's potential. I liked the sorrowful content of the piece - you have expressed the emotion really strongly throughout the entire piece. Your rhyming isn't perfect, but it can be seen that it is rhymed. The poem does flow really nicely though and the pace is perfectly for the piece. You descriptions were were well executed within the poem - you really set the gloomy scene which added to the feeling of grief and loneliness.

Good work! (: