Autonomous powered-descent guidance algorithm for the pinpoint Mars landing in the presence of various disturbances and uncertainties is necessary for next-generation Mars exploration rover mission. This paper proposes a novel two sliding-surfaces guidance scheme based on fixed-time stabilization technique, which is robust against unknown Martian atmospheric disturbances (with known upper bound). For a fixed-time pinpoint landing mission, the main advantage of the proposed guidance is that the landing mission reliability can be ensured that Martian surface collision would never encounter. The fuel efficiency can be guaranteed in the comparison with the offline fuel optimal solution. The capacity of avoiding collisions is guaranteed by the monotonic convergence design of the proposed sliding modes. Lyapunov stabilization theory is adopted to prove the global stability of the proposed guidance. Monte Carlo numerical simulations are implemented in a realistic scenario and the results confirm the collision avoidance capability, the fuel efficiency and the robustness of the proposed guidance.