This paper presents a gravity-balancing method for a two-degree-of-freedom (2-DoF) parallel robotic platform with variable payloads. The robotic platform is constructed with a parallelogram-based five-bar parallel mechanism, and it is gravity balanced by adopting a pair of gear-spring units (GSUs). Each GSU is formed by a geared seven-link mechanism with a tension spring. The parameters of the GSUs are realized from an analytical solution for approximate gravity balancing. The significance of the proposed method is that it can work with a range of payloads via energy-free adjustment and enables a choice in spring stiffness. In this paper, theoretical and practical models are provided to demonstrate the effectiveness of the proposed method. The simulation results showed that the actuator torque of a robotic platform with different payloads could be reduced by 98.2% with gravity balancing. Experimental tests with a prototype were conducted in which the measured driving force of the robotic platform along a trajectory showed a reduction of 87.1%.