The time-optimization problem for a linear non-stationary discrete-time system with first-order integral constraints on control is solved in the paper. For the case where the integral constraints are piecewise linear, the possibility of reducing the original problem to solving a number of linear programming problems is demonstrated. It is proved that, when the polyhedral approximation algorithm converges in the Hausdorff metric, the guaranteed solution converges to the optimal one in a finite number of iterations. Examples are given.