This paper presents a novel approach toward the inverse kinematics solution of the humanoid robot fingers with nonlinearly coupled joints, a challenging problem existing for years. Under an assumption that the coupled joint angles of the finger are the same, we first derive an approximate closed-form solution of the finger's inverse kinematics. Then, utilizing the approximate solution as the ancillary variable, we propose to solve the finger joint angles from this approximate solution rather than the fingertip position. Through analyzing properties of the approximate solution, it can be known that the coupled joint angles in the approximate solution play the most important role in the derivation of inverse kinematics. In practical implementation, a 1-D lookup table and the linear interpolation to the approximate solution are used to calculate the accurate joint angles. Simulation and experimental results demonstrate effectiveness of the proposed inverse kinematics method.