Zakah to non-Muslims

My neighbour is non-Muslim and he is very poor, some times his wife and children ask for some food or cash, old clothes. Can I give them Zakah?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
It is unlawful for you to give your Zakah to your neighbours as long as they are non-believers, unless the objective is to reconcile their hearts so that they become Muslims. The scholars state that in this respect the Muslim ruler is the person who makes the decision to give them as he is the only who can judge whether there is a benefit in giving them Zakah or not.
Anyway, we believe that you should not give it to them now and you should give your Zakah to its legal Muslim recipients. But if you feel like giving some alms to your non-believing neighbours you could do that. The Prophet told us to be kind to our neighbours.

Allah knows best.