Matrix multiplication is a fundamental operation of linear algebra and arises in many areas of science and engineering. This paper introduces an efficient parallel matrix multiplication scheme on N ${ imes}$ N mesh-connected SIMD array processor, called multiple hierarchical SIMD architecture (HMSA). The architectural characteristic of HMSA is the hierarchically structured control units which consist of a global control unit, N local control units configured diagonally, and $N^2$ processing elements (PEs) arranged in an N ${ imes}$ N array. PEs are communicating through local buses connecting four adjacent neighbor PEs in mesh-torus networks and global buses running across the rows and columns called horizontal buses and vertical buses, respectively. This architecture enables HMSA to have the features of diagonally indexed concurrent broadcast and the accessibility to either rows (row control mode) or columns (column control mode) of 2D array PEs alternately. An algorithmic mapping method is used for performance evaluation by mapping matrix multiplication on the proposed architecture. The asymptotic time complexities of them are evaluated and the result shows that paralle matrix multiplication on HMSA can provide significant performance improvement.