The Lorentz transformation of space and time between two inertial frames of reference is one of the pillars of the special theory of relativity. Until now, the Lorentz transformation equations have been considered on the base of one-dimensional motion between the inertial frames. The goal of this article is to extend the ordinary one-dimensional Lorentz transformation to motion along X-, Y-, and Z-directions, i.e., to achieve a space-time coordinate transformation in the three-dimensional (3D) space. We particularly discovered the modified Lorentz transformation equations along 3 directions, and this helped us to analyze the space contraction phenomena of a cuboid due to the relative motion between the inertial frames in the 3D space. As a final point, this study concluded that all length, breadth and height of a cuboid appeared to be shortened to the observer if there is the relative motion between the cuboid and an observer in the 3D space.