Anisotropic mesh adaptation has been used to accelerate computation in several engineering fields, and we show that it can also be used for topology optimization. We use a combination of filtered continuous sensitivities and filtered design variables to drive the mesh adaptation. The filtered design variables are computed for this purpose only, while the filtered sensitivities are used as input to the optimizer. We test mesh independence for a cantilever problem and also show results for two other test cases. Finally, speedup relative to isotropic adaptation is estimated at 50 using average element aspect ratios.