In this paper, a new method of model predictive control (MPC) for a multi-hop control network (MHCN) is proposed. An MHCN is a control system in which plants and controllers are connected through a multi-hop wireless network. In the proposed method, (i) control inputs and (ii) paths used in transmission of control inputs are computed with constant period by solving the finite-time optimal control problem. First, a mathematical model for expressing an MHCN is proposed. This model is given by a switched linear system, and is compatible with MPC. Next, the finite-time optimal control problem using this model is formulated, and is reduced to a mixed integer quadratic programming problem. Finally, a numerical example is presented to show the effectiveness of the proposed method.