Abstarct: Location problem is one of the most important is Operation Research and it has may application in the real world, such as locating of fire stations, police stations, emergency centers, hospitals, goods distribution centers, bus stops, subway stations, official centers, server in computer networks, post offices, garbage disposal centers, nuclear palnts and etc are most important applications of it. Two significant instances problem of location theory are p-median and p-center problem. in most location problems that are studied in recent decades, our data and information about the conditions of the problem were precise and clear, but in a real state and for real application, our data and information in this case are uncertain and vague. Thus fuzzy location problem on networks arise. In this dissertation we describe these problems and their solutions in the fuzzy mod, and offer a solution for the p-median problem when the weights of network's vertices are fuzzy numbers.