Control and trajectory generation of a 7 DOF anthropomorphic robot arm suffer from computational complexity and singularity problem because of numerical inverse kinematics. To deal with such problems, analytical methods for a redundant robot arm have been researched to enhance the performance of inverse kinematics. In this research, we propose an analytical inverse kinematics algorithm for a 7 DOF anthropomorphic robot arm. Using this algorithm, it is possible to generate a trajectory passing through the singular points and intuitively move the elbow without regard to the end-effector pose. Performance of the proposed algorithm was verified by various simulations. It is shown that the trajectory planning using this algorithm provides correct results near the singular points and can utilize redundancy intuitively.