We proposed a fast three-dimensional (3D) structured illumination photoacoustic microscopy (PAM). In the conventional PAM systems, the optical and acoustical beams need mechanical scanning to cover the whole area of interest for imaging imposing constraint on imaging speed. Using sinusoidal fringe illumination resulted in interference from a pair of tilted plane waves of different directions; capturing the resultant acoustic signal via a transducer array helped to improve lateral resolution and speed of the system while not degrading the depth-of-field (DOF). The sinusoidal structured illumination helps in more complete capture of spatial frequency components, which could be approved through a mathematical model of the system. Capturing more frequency components, in turn, results in improved frequency bandwidth and thus lateral resolution of the system. Simulation results show 5.4 dB improvements in image quality, based on the peak signal-to-noise ratio compared with a conventional structure.