Two-sided pyramid wavefront sensor (TSPWFS) is a kind of wavefront sensor with high spatial resolution and light energy utilization. To deeply study the principle of wavefront reconstruction of this wavefront sensor using wave optics theory, this paper deduces the diffraction theory of non-modulation TSPWFS and gives the analytic solution of linear reconstruction matrix for wavefront reconstruction. With numerical simulation the optimal distance between adjacent pupil image centers was determined. Also, wavefront reconstruction and closed-loop correction of static aberrations by using non-modulation TSPWFS as a wavefront sensor were simulated. The results show that non-modulation TSPWFS has three main advantages. i.e., it does not require measuring the response matrix in real optical setup, and can correct the optical systemic aberration, and can achieve stable closed-loop correction result. Additionally, non-modulation TSPWFS can be applied to a real adaptive optics system to detect wavefront.