Abstract: Prolate spheroidal wave function(PSWF)is non-sinusoidal and it is difficult for hardware implementation.The inefficiency and limitation of numerical algorithm restrict its theoretical development and application.For solving this problem,a new fast reconstructing algorithm for solving PSWF is proposed based on the sampling theorem.The reconstructing function and the approximate analytic solution are derived and the complexity of the algorithm is analyzed.The simulation result shows that the proposed method is more efficient than existing ones in the same precision.The proposed algorithm can be used for calculating numerical solutions of PSWF in any frequency bands and it is convenient for hardware implementation.