Autonomous close proximity operations (hovering, landing) in the low-gravity environment exhibited by asteroids are particularly challenging. A novel nonlinear landing guidance scheme has been developed for spacecrafts that are required to execute autonomous closed-loop guidance to a designated point on the asteroid surface. Based on High Order Sliding Mode control theory, the proposed Multiple Sliding Surface Guidance (MSSG) algorithm has been designed to take advantage of the ability of the system to reach the sliding surface in a finite time. High control activity typical of sliding control design is avoided resulting in a guidance law that is robust against unmodeled yet bounded perturbations. The proposed MSSG does not require any off-line trajectory generation and therefore it is flexible enough to target a large variety of points on the surface without the need of ground-based trajectory analysis. The global stability of the proposed guidance algorithm is proven using a Lyapunov-based approach. The behavior of the MSSG-based class of asteroid landing trajectories is investigated via a parametric analysis and a full set of Monte Carlo simulations in realistic landing scenarios. Based on such results, the MSSG algorithm is demonstrated to be very accurate and flexible. The proposed scheme is suitable for onboard implementation and deployment for asteroid landing and close proximity operations.