In the theoretical study and practical application of the instruments, the problem of nonuniform sampling signal reconstruction is an important research issue that is often confronted with. The use of polynomial approximation for reconstruction of traditional nonuniformly sampled signal is limited due to its huge computational cost. However, if the nonuniformly sampled signal to be processed has a periodicity, the processing speed can increase substantially. Hence, in this paper, polynomial approximation is introduced to reconstruct periodic nonuniformly sampled signal. Taking the advantage of periodic nonuniformly sampling’s recurrence, the polynomial approximation algorithm is simplified to reduce the algorithm’s computational cost significantly without sacrificing reconstruction precision. The simulation experiment for reconstructing periodic nonuniformly sampled signals is introduced to verify the feasibility and effectiveness of the simplified algorithm. The results show that the periodic nonuniform sampling signal is well reconstructed.