This paper presents a new method for rapid generation of time-optimal trajectories for asteroid landing via convex optimization. To overcome the nonconvex difficulty due to the free-flight time, a minimum-landing-error problem that can be convexified is proposed to serve as a gateway for solving the time-optimal control problem. The proposed method solves the reduced minimum-landing-error problem via convex optimization first and then searches for the minimum flight time through a combination of extrapolation and bisection methods. The effectiveness of the proposed methodology for rapidly generating time-optimal trajectories is validated through simulations of spacecraft landing on two asteroids with both finite thrust and low thrust.