A local discontinuous Petrov-Galerkin method is developed for nonlinear Schrödingerequations. Several kinds of solitons are simulated and related phenomena are discussed, such as the soliton propagation and collision, birth of solitons including standing soliton and mobile soliton, the bound state of N solitons. The algorithm simulates some narrow structures in soliton related phenomenon. Numerical examples show that the algorithm has high accuracy and can reach the optimal convergence order. Compared with local discontinuous Galerkin method, the local discontinuous Petrov-Galerkin method has high computational efficiency and simple computational formula.