This paper deals with the design, control, and implementation of a three-phase ac–ac mobile utility power supply using a matrix converter for airplane servicing applications. Using a matrix converter as a compact direct ac-to-ac converter can provide savings in terms of the size and cost of a mobile power supply compared to common back-to-back converters. Furthermore, using the proposed direct matrix converter eliminates the need for bulky electrolytic capacitors and increases the system’s reliability and lifetime. A finite control set model predictive control is used to generate a high-quality 115 V/400 Hz output voltage and a low-harmonic-distortion source current with a unity input power factor for various load conditions, including balanced, unbalanced, linear, and nonlinear loads. The predictive strategy is used to control the output voltage and source current for each possible switching state in order to simultaneously track the references. To achieve a further reduction in the system’s size and cost, an active damping strategy is used to compensate for the instability caused by the input filter in contrast to the passive method. Experimental tests were conducted on a prototype matrix converter to validate the performance of the proposed control strategy.