Abstract: An improved guide-weight method is presented to improve the computational efficiency of the guide-weight method on solving topology optimization problems, and the gray-filter method is introduced to restrain the gray-scale element which is generated in the optimization process. Since the optimization model was established based on RAMP（rational approximation of material properties, RAMP） scheme, and the guide-weight method was used as an algorithm combining for proposing the iteration formulas of the least compliance in multi objective topology optimization problems. First, the Lagrange multipliers solution method of the formulas were improved by the bi-sectioning algorithm. Then, with the purpose to suppress the generating of gray-scale element, the gray-scale filtering function was introduced into iterative formulas. Moreover, the proposed theory were extended to multi objective optimization problem, and ill-conditioning were avoided by normalizing single objective. Finally, two examples of multi objective optimizations problems were calculated respectively. The results calculated by examples demonstrate that using the proposed theory above can solve topology optimization problems with steady convergence, fast calculate speed and image sharpening.