In the last few years, memristor crossbar array is drawing increasing attention from the research community as a promising neuromorphic computing accelerator. In this work, we investigate the hardware acceleration of a sparse matrix vector (SpMV) multiplication engine based on memristor crossbar array. We demon strate that naive matrix coefficient mapping is infeasible and unpractical if the matrix has large dimensions. To combat this problem, we extend the traditional Cuthill-McKee algorithm used for matrix restructuring, and propose a generalized sparse matrix reordering (GSMR) technique, which leverages linear transformation to effectively break down any rectangular unsymmetrical matrices into minimum number of sub-blocks that fit into the reasonably sized crossbar array. Simulated results show that our proposed design achieves appealing p erformances in terms of speed and energy efficiency compared to both CPU and GPU platforms. In addition, a memristor crossbar array utilizing GSMR outperforms its counterpart with no-GSMR by 90% performance improvements and 44% energy reduction.