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In this Letter, we report, for the first time to our knowledge, on a continuous-wave, singly resonant optical parametric oscillator using an MgO: PPLN crystal pumped by an all-fiberized master-oscillator power amplifier structured amplified random fiber laser. An idler output power of 2.46 W at 3752 nm is achieved with excellent beam quality, and the corresponding pump-to-idler conversion efficiency is 9.6% at room temperature. The idler output power exhibits a peak-to-peak power stability better than 12.7%, and the corresponding standard deviation is better than 3.6% RMS in about 20 min at the maximum output power. Meanwhile, other characteristics of the generated signal and idler laser are studied in detail and not only offered an effective guide in the research of optical parametric processes in the case of a continuous spectrum, but also broadened the range of random fiber laser applications.