Police said the boy used homophobic language against the 49-year-old victim three times as he walked in the street.
Pc Helen Seymour said the Gloucestershire force took incidents of hate crime "extremely seriously".
"We thoroughly investigate any reports of hate crime - whether related to race or sexual orientation," she said.
"The majority of young people are fully aware that it is unacceptable to abuse people, particularly in racist and homophobic terms," she added.
"However, the minority who believe such abuse is amusing or acceptable should be warned that they could land themselves with a criminal record if they are caught."
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