In order to overcome numerical instabilities such as checkerboards,mesh-dependence in topology optimization of continuum structures,a new implementation combined with homogenization method without introducing any additional constraint parameter is presented.To overcome the shortcoming of continuous material distribution by the introduction of finite element approximation,moving least square or modified filter functions are adopted as interpolation function.The method can be viewed as nature extension of node-based homogenization method and named as material point homogenization method.Continuous size field and continuous density field are constructed and structural responses' sensitivities are derived.Several representative numerical examples are presented to demonstrate the capability and the efficiency of the proposed approach against some classes of numerical instabilities.