The electro-hydrostatic actuator (EHA) is a promising actuating apparatus used in flight control systems for more electric aircraft (MEA) due to its high power density and low maintenance. Since the reliability of the system decreases with increasing complexity, fault detection is becoming increasingly important. In this paper, an adaptive filter was designed based on a normalized least mean square (NLMS) algorithm, which could identify the resistance of the motor windings online to detect electrical faults in the EHA. Additionally, based on the analytical relationship between rotational speed and displacement, a rotational speed estimation method was designed. By comparing the actual rotational speed with the estimated one, hydraulic faults could be detected. To verify the efficacy of the aforementioned method, software was applied for the modeling and simulations, which included fault injection and detection. On this basis, an experimental platform was built and then subjected to a series of validation experiments. The results indicate that the fault detection method has the potential to detect electrical and hydraulic faults in an EHA.