The Lanczos algorithm is the most commonly used in approximating a small number of extreme eigenvalues for symmetric large sparse matrices. Global communications in MP(Message Passing) parallel computer decrease the computation speed. In this paper, we introduce the s-step Lanczos method, and s-step method generates reduction matrices which are similar to reduction matrices generated by the standard Lanczos method. One iteration of the s-step Lanczos algorithm corresponds to s iterations of the standard Lanczos algorithm. The s-step method has the minimized global communication and has the superior parallel properties to the standard method. These algorithms are implemented on Cray T3E and performance results are presented.