I don't know who this person is, or what your relationship is to him, but if you know him from school or a club, walk up to him once he starts following you again and call you names. Then say something loud and clear to him:
'I do not like what you are doing. Stop it.' Or: 'I do not like you belittling me, stop it.'
He does it again? Repeat process. Trust me, this may take a lot of trials, but keep consistent, keep a straight face (with that I mean, don't get angry, sad, upset, or even laughing in his face ^^; ), and a clear voice.
It might seem useless in the beginning, especially when it does not seem to even lessen his bullying, but he has bullied you for some time probably now, thus this situation might continue for a bit before it lessens or even stops.
This, or ignoring him entirely.
Eitherway, show him you couldn't care less about his behaviour, but if you say it, you're clear that all he's doing is wasting your (and his) time. When he gets the message, and even gets bored, trust me: He will stop.
If you rather not do this, then ignore him completely. This might be hard, but this has also been effective at least for me when I would be bullied. Though the most effective method is the previously first mentioned one, confronting him that you do not like it.
It is very important that eitherway, you be consistent. You can't one day decide to ignore him, and another day to go up to him and say you don't like it, and another day you try something else again. Be consistent. very important.
If it does escalate after whatever you decide to do, please keep mentioning it to your parents, or indeed involve the police.
I am indeed not sure if they would do anything about it. I mean, there are a lot of cases people tried getting police involved and they didn't do anything, because they didn't think of it being serious, but then please, keep pressing your parents to do something about it, or at least help you in some (other) way.
Make it even more clear to you it is still happening, it still bothers you, and in fact, it is starting to hurt you more and more, even because you feel they aren't taking it serious either. Communicate with them you are not happy with how things are going.
If the bully would indeed do something to threaten you, or physically harm you, and you have tried the above 'methods', please go to your parents and/or the police.
Once again, I do not know this person, or his relationship to you, but if it gets even more so out of hand, try to do everything you can in order to protect yourself with involving as many people (you trust/you should trust) as possible.
Eitherway, hope this advice helps you in some way