Abstract: The mathematical models of GPS positioning and velocity measurement are given.Then the iterative algorithm for GPS positioning and velocity measurement under normal condition is discussed based on Gauss-Newton method and the solution under the condition that there are only three visible satellites of G_DOP is too large is given.Finally,a complete iteration algorithm for GPS positioning and velocity measurement is obtained.This algorithm consists of two parts.In first part,the positioning solution is obtained iteratively and the satellite signal propagation time is renewed as the positioning solution is renewed in each iteration.In second part,the velocity is obtained by using the satellite signal propagation time and the normal matrix obtained in last iteration in the first part.