This paper studies a distributed collision-free formation control problem for networked quadrotors. The quadrotor dynamics is first derived and strictly linearized. Then, the quadrotor network consisting of multiple quadrotors with the dynamics and interconnection topology between them is defined, and a consensus-based formation control law is introduced as a nominal controller. Input conditions for collision avoidance are next derived based on control barrier functions, and as the main contribution, the conditions are modified to be distributed while explicitly considering the quadrotor dynamics. This distribution enables each quadrotor to calculate the actual control input by distributed quadratic programs. This paper also presents an advanced collision avoidance method for severe situations. The effectiveness of the present controllers is demonstrated via simulation.