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Beam pointing error caused by ship motion over the ocean affects the tracking performance of the ship-borne phased array radar. Due to the dynamic nature of the sea environments, the ship-borne phased array radar must be able to compensate for the ship’s motion adaptively. In this paper, the adaptive α-β-γ filter is proposed for the ship-borne phased array radar to compensate for the beam pointing error and to track the air target. The genetic algorithm (GA) and the particle swarm optimization (PSO) methods are applied to estimate the gain parameters of adaptive α-β-γ filters, while achieving the optimum objective of minimum root mean square error (RMSE). The roll and pitch data measured from a gyroscope of the sea vehicle and generated from ship motion mathematical model are used in the experiments. The tracking accuracy of adaptive α-β-γ filter using the GA method is compared with PSO method under different ship motion conditions. The convergent time and tracking accuracy of ship-borne phased array radar using the proposed GA based adaptive α-β-γ filter are also compared with the adaptive extended Kalman filter (AEKF). Finally, it is proved that the proposed GA based adaptive α-β-γ filter is a real time applicable algorithm for ship-borne phased array radar.