This paper presents a data-driven method to obtain an approximate solution of the finite-horizon optimal control problem for linear time-varying discrete-time systems. Firstly, a finite-horizon Policy Iteration method for linear time-varying discrete-time systems is proposed. Then, a data-driven off-policy Policy Iteration algorithm is derived to find approximate optimal controllers when the system dynamics is unknown. Under mild conditions, the proposed data-driven off-policy algorithm converges to the optimal solution. Finally, the effectiveness of the derived method is validated by a numerical example.