In this paper we present an Overlapped Block Gauss-Seidel (OBGS) algorithm for the solution of large scale LSEs (Linear System of Equations) based on array architecture which we have already proposed. Better partitioning for processor array usually requires (1) balanced block size, and (2) minimum coupling between blocks for better convergence. These conditions can well be satisfied by overlapping some variables in computation algorithm. The mathematical implication of overlapped partitioning is discussed at first, and some examples show the effectiveness of OBGS algorithm. Conclusion points out that the convergence properties can well be improved by proper choice of overlapped variables. An efficient algorithm is given for choosing block and variables in order to realize above conditions.