A fundamental problem in conventional photography is that movement of the camera or captured object causes motion blur in the image. In this research, we propose coding motion-invariant blur using a programmable aperture camera. The camera realizes virtual camera motion by translating the opening, and as a result, we obtain a coded image in which motion blur is invariant with respect to object velocity. Therefore, we can reduce motion blur without having to estimate motion blur kernels or requiring knowledge of the object speed. We model a projection of the programmable aperture camera and also demonstrate that our proposed coding works using a prototype camera.