Abstract: Flexible landing is a new way to prevent rebound and overturning in weak gravity environments of small celestial bodies and improve landing safety on these bodies. To realize obstacle avoidance of the flexible lander during the landing process, an adaptive curvature guidance method combined with convex programming and the concept of virtual safety boundary was proposed. Based on the geometric convex trajectory obtained through curvature guidance, a virtual safety boundary related to the structural characteristics of the flexible lander was constructed. The shape of the boundary was adaptively adjusted according to terrain obstacle information, and the optimal obstacle avoidance trajectory was solved via successive convex programming technique. The result of numerical simulation shows that the method proposed in this paper possesses satisfactory obstacle avoidance capability for the flexible landing mission in complex terrain conditions, which further improves the landing safety on small celestial bodies.