Abstract: To resolve the numerical instabilities in continuum topology optimization, a material point topological variable is adopted to describe the existence or null of the material point and its vicinity. A new bidirectional evolutionary topology optimization method using material point description is proposed. Based on filtering scheme, a new manner of topological variable field is constructed. The checkerboard patterns are eliminated naturally in the topological optimization model. A new concept of sensitivity density is redefined to be appropriate to different element types and mesh grids. Two-dimensional numerical examples show that the proposed method is feasible and effective in the topological optimization design of continuum structures.