Nonlinear impairment is one of the critical limits to enhancing the performance of high-speed communication systems. Traditional digital signal processing (DSP)-based nonlinear channel equalization schemes are influenced by limited bandwidth, high power consumption, and high processing latency. Optoelectronic reservoir computing (RC) is considered a promising optical signal processing (OSP) technique with merits such as large bandwidth, high power efficiency, and low training complexity. In this paper, optoelectronic RC was employed to solve the nonlinear channel equalization problem. A parallel optoelectronic RC scheme with a dual-polarization Mach-Zehnder modulator (DPol-MZM) is proposed and demonstrated numerically. The nonlinear channel equalization performance was greatly enhanced compared with the traditional optoelectronic RC and the Volterra-based nonlinear DSP schemes. In addition, the system efficiency was improved with a single DPol-MZM.