Direct air-cooling is considered as a promising technique in power generation because of its distinct water-saving advantages, where ambient air is utilized instead of water, to cool down the exhaust steam in the direct air-cooling condenser. However, the relatively poor heat transfer characteristics and thermodynamic properties of air also brings higher backpressure in the direct air-cooling generating unit compared with conventional water-cooling generating unit, as well as the sensitivity of condenser performance to meteorological and ambient conditions. Therefore, the unit backpressure control for the direct air-cooling generating unit has been a challenging task in the recent years. To this end, a control-oriented mechanism dynamic cold-end system model is built for the direct air-cooling generating unit in this paper. The modified moving boundary method is utilized to capture the dynamic process of exhaust steam condensation in the condenser, wherein a time-variant mean void fraction is adopted to enhance model accuracy and robustness. Validation results with operating data have shown the established model can capture the dynamics of direct air-cooling cold-end system with satisfied accuracy. Based on the established model, a model predictive controller with feedforward compensation is proposed to keep unit backpressure steady at the desired set-point while suppressing the time-varying stochastic ambient temperature disturbances by regulating the rotation speed of fan array appropriately. The simulation results have verified the merits and effectiveness of the proposed strategy in achieving both satisfactory backpressure regulation and disturbance rejection performance.