The independent continuous mapping(ICM) method is integrated into element free Galerkin method and a new implementation of topology optimization for continuum structure is presented. To facilitate the enforcement of the essential boundary condition and derivative of various sensitivities, a singular weight function in element free Galerkin method is introduced. Material point variable is defined to illustrate the condition of material point and its vicinity instead of element or node. The topological variables field is constructed by moving least square approximation which inherits the continuity and smoothness of the weight function. Due to reciprocal relationships between the topological variables and design variables, various structural responses sensitivities are derived according to the method for calculating the partial derivatives of compound functions. Numerical examples indicate that checkerboard pattern and mesh-dependence phenomena are overcome without additional restriction methods.