A collision determination device includes a target cell designation unit that designates a target cell for a voxel model which represents the shape of a first object. A determination test point generation unit generates determination test points for the target cell. A spatial curve creation unit creates a spatial curve as the trajectory curve of a determination test point. A curve intersecting determination unit determines whether or not each boundary element of a boundary representation model representing the shape of a second object is intersecting the spatial curve. A distance computation unit computes the closest distance from the spatial curve to the boundary surface of the boundary representation model. A collision determination unit determines, based on the determination result and the computation result, whether there is a possibility of collision between both objects.