For the visualization of a 4-D object, information in 4-D space is obtained by projecting a 4-D space onto a 3-D space. Previous researches mainly paid attention to the geometrical information of a single 4-D object in 4-D space. Our research aims to develop a visualization system for physical phenomena in 4-D space and to study the human spatial cognition of the 4-D space through the projected 3-D space. In this research, we focus on a collision of two 4-D objects in 4-D space and develop an algorithm for the collision detection between two 4-D objects to be displayed in 3-D space. In our developed algorithm, a 4-D object is defined as a mesh data of tetrahedrons, and a tetrahedron-based collision detection algorithm is performed by a combination of half-space tests with the use of 5-D homogeneous processing to enhance the calculation accuracy of the collision detection. The results of the collision detection between the 4-D objects are presented.