Constrained Sensitivity Filtering Method (CSFM) has been proposed to save computational expenses in topology optimization. The sensitivity filtering technique is widely adopted to avoid numerical instabilities. Because the filtered sensitivity values are recalculated from the normalized density values and the sensitivity values from within a fixed range of neighborhoods, the values are sometimes completely different from the original ones. Thus, the idea of the CSFM is to control the change of filtered sensitivity values based on the previous iterations. By controlling the changes of filtered sensitivity values within certain limitation, optimal layouts can be obtained with lower compliance and the computational expenses can also be reduced in comparison to that by conventional topology optimization. The computational expense with CSFM topology optimization could be reduced by up to 85%. The numerical examples established that CSFM topology optimization has improved the numerical efficiency and effectiveness.