Cable-driven hyper-redundant manipulator (CDHM) with flexible and compliant configuration has high maneuverability in a tight space owing to its multiple degrees of freedom (DOFs). However, an increase in the DOFs of the manipulator makes it very challenging to solve its inverse kinematics. The present work proposes a novel adaptive piecewise geometry method to solve the inverse kinematics of the CDHM. The corresponding computation efficiency will be much lower for traditional methods, i.e., the generalized inverse of the Jacobian matrix and artificial neural network method. When the end-effector of the manipulator is required to move with a larger range, Joint angle physical limit need to be considered and the proposed method can select the optimal arc configuration to solve the inverse kinematics aiming at reducing joint overrun. An adaptive adjustment coefficient is further introduced to optimize the configuration so that joint motion more reasonable as well as avoid singular configuration. The geometry and joint parameters solved with the proposed novel method are then compared to those of the existing method with the same desired target position to verify the effective of the proposed novel method. Finally, a 12-DOFs hyper-redundant manipulator physical prototype is built, and corresponding experimental results show that with the novel solution method, the manipulator end can precisely reach the expected target position with significantly less computational complexity, which is beneficial to improve real-time control efficiency of the CDHM in practical applications.