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This study presents a multilayer interval type-2 fuzzy controller for controlling quadcopter unmanned aerial vehicles, and its main contribution is the design of a multilayer structure in the membership function, which can improve the learning ability and flexibility of the designed network. With the multilayer structure, the proposed network can reduce the number of rules while ensuring the control system performance. Also, the proposed network parameters are updated online using adaptive laws, which are obtained using the gradient descent method, and a Lyapunov stability function is used to guarantee system stability. Furthermore, the learning rates of the proposed network are optimized using the Jaya algorithm. Numerical experimental results were conducted on the trajectory tracking control of a quadcopter unmanned aerial vehicle to illustrate the effectiveness of the proposed control method.