The inverse kinematics of continuum robot is an important factor to guarantee the motion accuracy. How to construct a concise inverse kinematics model is very essential for the motion control of continuum robot. In this paper, a new method for solving the inverse kinematics of continuum robot is proposed based on the geometric and numerical method. Assumed that the deformation of the continuum robot is Piecewise Constant Curvature model (PCC), the envelope surface of the continuum robot based on single-segment is modeled and calculated. The clustering method is used to calculate the intersection of the curves. Then, a distinct sequence is designed for solving the inverse kinematics of continuum robot, and it is also suitable for the multi-segment continuum robots in space. Finally, the accuracy of the inverse kinematics algorithm is verified by the simulation and numerical experiment. The experiment results illustrate that this algorithm is with higher accuracy compared with the Jacobian iterative algorithm.