The present study aims to derive modified geodesic equation in non-commutative space time. Snyder developed a model for non-commutative space time which provides a suitable technique of quantum structure of the space. We extend Tetrad formulation of general relativity to non-commutative case for complex gravity models. We derive geodesic equation on the k-space time in Non-commutative space, which is a generalization of Feynman’s approach. It has been shown that the homogeneous Maxwell’s equations may be derived by starting with the Newton’s force equation and generalized to relativistic. We show that the geodesic equation in the commutative space time is a suitable for generalization to κ -space time in κ -deformed space time. It shown that the κ-dependent correction to geodesic equation is cubic in velocities.