Global warming, increase in environmental pollution, and high cost of electrical power generation using fossil fuels are considered the most important reasons for the application of renewable energy power plants (REPPs) around the world. In recent years, a new generation of REPPs called hybrid renewable energy power plants (HREPPs) has been implemented in order to have higher efficiency and reliability than conventional REPPs such as wind power plants and photovoltaic power plants. The HREPPs include two or more renewable energy generation units such as wind turbine generation units, and PV generation units. In case of high penetration of these types of power plants, the most common tasks of synchronous generators should be supported by them. One of these tasks is the ability to reduce the low-frequency oscillation (LFO) risk through power oscillation damper such as the power system stabilizers of synchronous generators. In this paper, a novel method is proposed for LFO damping by HREPPs, which is based on the design of an optimal power oscillation damper (OPOD) implemented in the generic HREPP controller model. The structure of the proposed OPOD is a 2nd-order single-input lead-lag controller, and its performance is investigated in a modified two-area test system. The simulation results show the proper performance of the HREPP for LFO damping using the proposed OPOD in the various loading levels and different short circuit ratio values.