Translation:His hobby is listening to music.
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Yes it is grammatically correct, but in this case it is probably better to say "listening" because it is his hobby and therefore it is likely to be an ongoing or habitual practice, and so the continuous form of the infinitive is used. Using "listening" makes it clear that it is referring to something that he is already doing. However if you were talking about something he wanted to do in the future you would be more likely to use the "to" form of the infinitive e.g. "his ambition is to become a ...." because he is not doing it yet.
In Chinese, some characters can have multiple pronunciations - these are called polyphones. 乐 for example is pronounced "yuè" when used in 音乐 (yīnyuè, music) however it can also be pronounced as "lè" when used in 快乐 (kuàilè, happy). Basically the pronunciation of the character is determined by the context of the sentence.
Here's a useful page explaining some of the main Chinese polyphones that might be helpful: