This paper proposes a novel avoidance method called the three-dimensional velocity obstacle method. The method is designed for unmanned aerial vehicle applications, in particular to autonomously handle uncoordinated multiple encounters in an integrated airspace, by exploiting the limited space in a three-dimensional manner. The method is a three-dimensional extension of the velocity obstacle method that can reactively generate an avoidance maneuver by changing the vehicle velocity vector based on the encounter geometry. Adverse maneuvers of the obstacle are anticipated by introducing the concept of a buffer velocity set, which ensures that the ownship will diverge with sufficient space in case of sudden imminence. A three-dimensional resolution is generated by choosing the right plane for avoidance, in which the unmanned aerial vehicle conducts a pure turning maneuver. Implementation of the three-dimensional velocity obstacle method is tested in several simulations that demonstrate its capability to resolve various three-dimensional conflicts. A validation using Monte Carlo simulations is also conducted in stressful superconflict scenarios, which results in zero collisions occurrences for the entire 25,000 samples.