In this paper, a prescribed-time extended state observer (PTESO) is constructed for a three degree-of-freedom (3-DOF) parallel ship-borne platform to estimate the platform’s total disturbances, including dynamic uncertainties, unknown time-varying external disturbances and coupling between the platform motion state variables. The constructed PTESO offers the advantages of converging within a prescribed time, suppressing initial peaking phenomenon and easy implementation. Furthermore, a PTESO based PD-like robust stabilization control law is designed, which maintains the support surface of the platform at a given horizontal position and orientation in the inertial space. Theoretical analyses show that the resulting closed-loop stabilization control system is stable. Simulation results with comparisons are presented to verify the effectiveness of our proposed robust stabilization control strategy.