Lower-order large aberrations, such as defocusing and spherical aberrations, caused by uneven temperature distribution inside an optical telescope system and mirror thermal deformations, seriously reduce the detection capability of an optical system. Herein, a method for wavefront detection that combines the phase diversity method with defocusing grating is introduced. In addition, a hybrid particle swarm algorithm that combines a linear descending weight particle swarm optimization with tabu search is proposed. The optimization performance of the algorithm is verified by simulation. Two images are acquired using a combination of the phase diversity method and defocusing grating, enabling the wavefront to thereafter be reconstructed and the wavefront aberration to be estimated by solving the objective function using hybrid particle swarm algorithm. The simulation results show that the proposed algorithm can solve the objective function for the wavefront aberration with an RMS value below 0.859λ. After optimization, the wavefront residual error reaches the order of 10 ^-3 and convergence is achieved after approximate 3 iterations. This result satisfies the correction accuracy of low-order large aberration.