Apodization has found many important applications in imaging and optical communication. Traditional apodization methods are based on the phase or amplitude modulation, suffering from either narrow working bandwidth, or reduced spatial resolution. Here, a broadband achromatic metasurface filter is proposed to realize apodization imaging without sacrificing the spatial resolution. With this filter, a nearly dispersionless phase modulation in the entire visible waveband can be achieved. The simulated results indicate that the focusing efficiency of the metasurface filter is twice larger than that of the phase filter and the imaging contrast can be improved by three times with the metasurface filter compared to the Gaussian filter. The sidelobes in the point spread function can also be efficiently suppressed to the scale of 10-5 in the whole visible spectrum ranging from 400 nm to 700 nm with our design. Additionally, the resolution of diffraction limit or even sub-diffraction can be achieved with this method.