Abstract: This paper discusses the problem of finding Euler circle covering some certain edges in urban traffic network. It comes from path selection problem in Demand Responsive Transit System, in which passengers distribute at certain streets. By providing two organization methods, settling a bus as soon as the reserving passengers getting certain amounts, say bus capacity, or settling a number of buses when the reserving passengers get more. This paper solves the first case by providing an algorithm to find the minimum Euler circle covering some certain edges. Then it offers some methods to transform the second case to a dynamic planning problem.