Given a time horizon parameter h and an object set O, predictive collision detection finds all the object pairs < oi, oj, ti > which will collide in the future time interval [t,t + h] (where 1 - i, j, - n, ti - [t, t + h]). Although there are a number of state-of-the-art approaches to solve collision detection problems, predictive collision detection is addressed for the first time. In this paper, we propose a grid-based predictive collision detection algorithm (GPCD), which is a general technique for the efficient detection of the collision of object pairs in a future time interval. GPCD first determines a candidate list which stores the object pairs having a non-zero probability to collide in a future time. Then, GPCD achieves low running time based on two pruning strategies: (i) space intersection test and (ii) time intersection test. These two pruning strategies eliminate most of the false collision cases in an initial filtering phase. In the refinement phase, a bounding-volume tree is applied to refine the detection results. Our experiments show that GPCD works well for the purpose of predictive collision detection.