In this paper we study an efficient multilevel algorithm for implementing the linear sampling method in inverse obstacle scattering problems. The algorithm performs a multilevel investigation of the concerned domain while avoiding the need for exploring the meshgrid point by point. The algorithm requires to solve only O(n^N − 1) far-field equations for the concerned problem in R^N (N=2,3) instead of the original O(n^N) equations. We present the results of numerical experiments to illustrate the efficiency and effectivenss of the algorithms.