The time-optimization problem is solved for linear discretetime systems with linear control constraints. The optimality criterion of the process is formulated in terms of null-controllable sets, and it is demonstrated the exponential computational complexity of the exact solution. To increase the efficiency of the solution, a method for constructing suboptimal control based on polyhedral approximations of null-controllable sets is proposed. The use of a polyhedral approximation algorithm with polynomial time complexity makes it possible to reduce the computational complexity of solving the time-optimization problem from exponential to linear depending on the time-optimization. The effectiveness of the theoretical results is demonstrated by solving the problem of the fastest correction of the satellite’s orbit. The satellite is considered as a material point located in the neighborhood of a circular orbit, controlled by low-thrust engines of limited power.