This paper proposes an original intelligent robust control method for a kind of aviation electric fuel pump (AEFP) systems, in order to realize on-demand fuel supply for aircraft engines, accurately and robustly. By considering the feature of AEFP, the intelligent robust control method is in a cascaded structure, which combines a novel second order integral sliding mode control (SOISMC) approach with uncertainty and disturbance estimator (UDE) strategy, together with a new multi-objective variable speed grey wolf optimization algorithm (MOVSGWO). To let the current loop of AEFP possess both rapidity and robustness, the SOISMC is presented based on an innovative second order integral sliding mode manifold. To realize that AEFP has strong robustness to both the changing of speed command and the pulsation in fuel pump, UDE is utilized for the speed loop of AEFP. The primary parameters in the intelligent robust controller, namely, UDE-SOISMC controller, are optimized by MOVSGWO. The MOVSGWO is a modified grey wolf optimization algorithm with variable speed by particle swarm optimization. Mismatched uncertainties and disturbances in AEFP can be handled by the proposed robust method. The calculation of instantaneous flow and dynamic torque in AEFP is illustrated. Simulation and experimental results verify the effectiveness of the UDE-SOISMC method. [ABSTRACT FROM AUTHOR]