We have studied the variational matrix product state (MPS) algorithm to find the ground state of many-body systems. For that, we discuss how to represent the many-body quantum states with use of the MPS formalism and investigate its structure related to the ground state energy of the system. Also, we show a few specific examples to disassemble the operator into the class of the matrices in matrix product operator representation. After programming an algorithm for the matrix simulation, we test the accuracy of its algorithm for s = 1/2 one-dimensional Heisenberg model as calculating the energy difference between variational MPS method and DMRG method. Using the method, we simulate the ground energy for one-dimensional XX model and the Majumdar-Ghosh model. (C) 2016 Elsevier B.V. All rights reserved.