When UAVs formation flying in 3-D dynamic environment following the reference path, obstacles may popup and collisions may happen. To solve this problem, a distributed formation keeping method with obstacle/collision avoidance is proposed. The virtual structure approach and nonlinear model predictive control(NMPC) method are applied to design the distributed formation controller. To achieve collision avoidance between UAVs with consideration of communication delay, a spatial penalty function with the priority strategy is designed. According to the simulation results,the distributed NMPC formation controllers can make the UAVs steer clear of static/moving obstacles with no collisions between UAVs, and the formation keeps following the reference path after finishing obstacle avoidance.