In various applications of speech transmission and procession, there is always a possibility of loss of samples. The iterative algorithm of Papoulis-Gerchberg is famous algorithm for solving the lost samples recovery problem. The algorithm, however, is usually slowly convergent. This paper presents a new approach for restoring lost samples with preprocess for meeting boundary conditions of discrete Fourier transform (DFT) in the iteration of Papoulis-Gerchberg algorithm. The simulation indicates the mean square error (MSE) of the recovery and the convergence rate with the preprocess concept is much better and faster than that without preprocess concept.