This paper proposes an adaptive backstepping control algorithm for electric braking systems with electromechanical actuators (EMAs). First, the ideal mathematical model of the EMA is established, and the nonlinear factors are analyzed, such as the deformation of the reduction gear. Subsequently, the actual mathematical model of the EMA is rebuilt by combining the ideal model and the nonlinear factors. To realize high performance braking pressure control, the backstepping control method is adopted to address the mismatched uncertainties in the electric braking system, and a radial basis function (RBF) neural network is established to estimate the nonlinear functions in the control system. The experimental results indicate that the proposed braking pressure control strategy can improve the servo performance of the electric braking system. In addition, the hardware-in-loop (HIL) experimental results show that the proposed EMA controller can satisfy the requirements of the aircraft antilock braking systems.