Under the Light of the Moon [Capitalize all significant words in a title]

Under the light of the moon,

The pain of the heart is not felt... [An ellipsis contains 3 periods.]

The sound of guitar is joyous...

And the night is getting fleeting ["getting" is not wrong, in my opinion, "fleeting is more poetic] far from the dusk.

(Could Can you please correct my English?)

What you wrote is a poem and so each sentence/phrase should be on a new line with its first letter capitalized. Your poem is well written.  Good job :)

Under the light of the moon

Under the light of the moon, the pain of the heart is not felt..the sound of the guitar is joyous..and the night is getting far from the dusk.

(Could you please correct my English?)

That is the only thing I see that MAY need to be added.  You could get away with not adding "THE"

Good Job