Elijah Mitchell, 23, was upset that 30-year-old Arturo Jose Rodriguez Marcano was sleeping in Steuben Playground, according to the Brooklyn District Attorney's Office.
Marcano -- who was from Venezuela -- had been living in a tent inside the park along with other migrants.
Mitchell and Marcano had gotten into a fight back on July 18, investigators said.
Three days later, police say, Mitchell shot Marcano in the chest and then fled the scene.
Marcano was transported to Methodist Hospital, where he was pronounced dead shortly upon arrival.
"This defendant allegedly came to the location where the victim was staying, armed with a gun, to settle a score," said Brooklyn District Attorney Eric Gonzalez. "This premeditated and coldblooded homicide is outrageous on many levels, not least because the alleged motive was hatred towards new arrivals to our city."
Mitchell is facing multiple charges.
If convicted, he faces a maximum sentence of 25 years to life in prison.
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