Due to factors such as the limited capabilities of the actuators， one needs to generally consider the effect of constraints on both attitude and angular velocity when addressing the attitude consensus control problem of multiple unmanned aerial vehicles （UAVs）. However， the constraints on both attitude and angular velocity pose a challenge to the design of effective attitude consensus controllers for multiple UAVs. To address such an issue， this paper introduces a finite-time attitude consensus controller for multiple UAVs under state constraints including the constraints on both attitude and angular velocity. Specifically， by using tools from nonsmooth analysis and algebraic graph theory， the paper develops a class of finite-time attitude consensus control strategies. In addition， combined with the barrier Lyapunov function （BLF） technique， it constructs a novel attitude consensus tracking controller. Theoretical analysis demonstrates that， under attitude and angular velocity constraints， the proposed controller enables the attitude of all UAVs to track the desired attitude within a finite time. Notably， the proposed method offers advantages such as simplicity of structure， adaptability to user-defined constraints， and fast convergence. Simulation results indicate that the proposed controller achieves finite-time consensus tracking of the desired attitude under constraints on attitude and angular velocity.