Differential wavefront lidar is a lidar system for measuring the atmospheric optical turbulence intensity based on wavefront differential jitter variance of a laser echo detected by the two-aperture telescope. To evaluate and optimize the detection performance of this system for atmospheric optical turbulence, numerical simulations have been carried out. According to the wave optics theory, atmospheric turbulence phase screen model, and atmospheric extinction model, the propagation of laser beam in vertical atmospheric path is simulated. Combined with the optimized design of grid sampling, the intensity distribution of laser beam at different positions along the propagation path is obtained. Based on the principle of incoherent light source imaging, the distributions of two spot images on the detector are obtained according to the backscattered light intensity distributions at different transmission paths. According to the simulation results, we find that the degree of beam wavefront distortion is deepened with the increase of turbulence intensity. The diameter of the imaging spot decreases with the increase of the detection height. When the detection height is 10 km, the diameter of the imaging spot decreases to 2.45×10 ^-4 m. By comparing the simulated inversion results with the results of the input HV_5/7 (Hufnagel Valley 5/7) in simulation, we find that the two have high consistency, which preliminarily proves the reliability of the principle and method of atmospheric turbulence detection by using the differential wavefront lidar.