Increasingly, robots have more degrees of freedom (DOF), imposing a need for calculating more complex dynamics. As a result, better efficiency in carrying out dynamics computations is becoming more important. In this study, an efficient method for computing the joint space inertia matrix (JSIM) for high DOF serially linked robots is addressed. We call this method the Geometric Dynamics Algorithm for High number of robot Joints (GDAHJ). GDAHJ is non-symbolic, preserve simple formulation, and it is convenient for numerical implementation. This is achieved by simplifying the way to recursively derive the mass-matrix exploiting the unique property of each column of the JSIM and minimizing the number of operations with O(n2) complexity. Results compare favorably with existing methods, achieving better performance over state-of-the-art by Featherstone when applied for robots with more than 13 DOF.