Collision avoidance for multiple aircraft can be stated as a problem of maintaining safe distance between aircraft in conflict. Optimal collision avoidance problem seeks to minimize the given cost function while simultaneously satisfying constraints. The cost function could be a function of time or control input. This paper addresses the trajectory time-optimization problem for collision avoidance of unmanned aerial vehicles(UAVs). The problem is difficult to handle in general due to the two-point boundary value problem subject to dynamic environments. Some simplifying algorithms are used for potential applications in on-line operation. Although under possibility of more complicated problems, a dynamic problem is transformed into a static one by prediction of the conflict time and some appropriate assumptions.