The five-equation model of multi-component flows has been attracting much attention among researchers during the past twenty years for its potential in the study of the multi-component flows. In this paper, we employ a second order finite volume method with minmod limiter in spatial discretization, which preserves local extrema of certain physical quantities and is thus capable of simulating challenging test problems without introducing non-physical oscillations. Moreover, to improve the numerical resolution of the solutions, the adaptive moving mesh strategy proposed in [Huazhong Tang, Tao Tang, Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws, SINUM, 41: 487-515, 2003] is applied. Furthermore, the proposed method can be proved to be capable of preserving the velocity and pressure when they are initially constant, which is essential in material interface capturing. Finally, several classical numerical examples demonstrate the effectiveness and robustness of the proposed method.