Abstract: The parachute deployment condition during the terminal entry phase in Mars landing missions exhibits critical impact on landing precision. In this article, aiming at the requirements of safe parachute deployment and accurate landing, a multi-dimensional parachute deployment box for determining deployment condition during Mars landing is proposed. First, an extreme-range optimization model is established, synthesizing the dynamics and constraints of both parachute descent and powered descent phases. Then, on the basis of the two-dimensional altitude-velocity deployment box, a multi-dimensional parachute deployment box characterized by altitude, velocity, flight-path angle, and extreme range is constructed through the integration of extreme range information. Furthermore, an evaluation index for landing precision is formulated and a deployment control logic is proposed for minimizing landing deviation. Finally, the proposed deployment box is simulated in a Mars landing mission. The results demonstrate that the proposed box effectively satisfies safe deployment and landing precision demands, eliminating the range-to-go error at the terminal of the entry phase.