with improvements on automation, computer, electronics and other technologies, applications of unmanned aerial vehicles (uavs) have expanded from pure military field to civilian areas. as a multirotor aircraft, a quadrotor uav has the advantages of simple structure, small size, high manoeuvrability, etc. on the basis of summarizing the current research situation of the quadrotor uav, a deep research has been conducted on the attitude control system of the quadrotor uav and two controllers are proposed to generate a stable performance: back-stepping controller, adaptive fuzzy back-stepping nonlinear controller. the quadrotor uav consists of two pairs of rotors and propellers, which can generate thrust and air drag. the dynamic model is derived using the euler-lagrangian method and newton method with 6 degrees of freedom. to represent the model of the quadrotor, euler angles representation is first derived. however, facing the gimbal lock drawback of euler angles representation, unit quaternion representation is then discussed afterwards. in normal situations, model parameter uncertainties and external disturbances would affect the system output. due to this problem, an adaptive fuzzy strategy is designed to approximate the uncertain model using back-stepping techniques with the lyapunov stability theorem. firstly, simulations are used to prove the mathematical feasibility. and then experimental results will be provided to illustrate the satisfactory performances of the proposed approach in real time.