Many industrial and engineering problems are transformed into optimization problems and solved using various numerical based methods. One of the frequently used method is the Steepest descent algorithm which converge to the solution in only one iteration, given the current point and provided the quadratic function is positive definite. However, this method is not suitable for large scale functions because of lack of gradient information and high computational cost. This study aims to suggest a new conjugate gradient algorithm for motion control of robotic manipulators and unconstrained optimization models. The convergence result of the new algorithm would be discussed under some suitable conditions. Computational simulations are carried out on the discrete-time kinematics equation of a two-joint planar robot manipulator to illustrates the efficiency of the algorithm. The algorithm was further extended to unconstrained optimization problems in addition to motion control of robotic manipulators. Preliminary results prove that the new algorithm is efficient compared to the existing CG algorithm. The comparisons are made using the set of 50 standard benchmark functions including number of iterations and CPU time.