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Since the three-dimensional motion control of UAV swarms is quite complex, a three-dimensional flocking control algorithm based on biological collective behaviors and Reynolds rules is proposed. Most of previous research simplified UAV swarms as two-dimensional motion, but which is not in accordance with practical control demand. Therefore, flocking algorithm and artificial potential field algorithm are used in three-dimensional UAV swarms. Three-dimensional UAV swarms simulation model is built. Besides, whether the two algorithms are effective in controlling the three-dimensional UAV swarms through simulation in different initial conditions. The results show that the two algorithms have some effect on flocking motion control in three-dimensional space, but they need harsher terms than in two-dimensional plane. At the same time, it has been found that the intelligent algorithm is better in cohesion control but the artificial potential field algorithm is better in separation control. As a result, a new flocking control algorithms combined the two algorithms is proposed that the algorithm uses flocking algorithm in long distance cohesion control and artificial potential field algorithm in short distance separation control, which performs better in three-dimensional UAV swarms control.