With the advantages of high energy density, high accuracy, and fast response, smart material-driven electro-hydrostatic actuators (SMEHAs) have attracted significant attention in recent years. However, the low flow rate of SMEHAs constrains their application. One potential solution to enhance the flow rate is to increase the number of smart material-actuated pumps. In view of this, this paper proposes a new configuration of an electro-hydrostatic actuator equipped with four magnetostrictive-actuated pumps (FMEHA) to achieve a large flow rate. The mathematical model of the FMEHA is established to investigate the driving phase matching between pumps and the active flow distribution valve. The physical prototype of FMEHA is fabricated. Simulations and experiments are conducted to assess its performance under various driving parameters, including the number of pumps, driving phase, frequency, and amplitude. The optimal driving parameters for the FMEHA are determined based on the results obtained. Experimental findings demonstrate that with a driving phase of 340°, a frequency of 250 Hz, and an amplitude of 20 A, the FMEHA achieves a maximum flow rate of 6.2 l/min.