This brief presents an efficient algorithm to solve time-optimal point-to-point motion control problems for discrete-time linear time-invariant systems with linear system constraints. Instead of using a bisection algorithm and solving a linear feasibility problem in each iteration, this brief proposes an iterative algorithm that is based on the Newton-Raphson method. In each iteration a maximum range problem is solved, maximizing the travel range of a system for given motion time and system constraints. Although each iteration of the proposed algorithm is computationally more expensive than an iteration of the bisection algorithm, numerical examples demonstrate that the presented approach is generally more efficient thanks to a great reduction in the number of optimization problems to be solved.