This paper introduces a high single-pulse energy, narrow-linewidth mid-infrared self-optical parametric oscillator (mid-IR SOPO) with a cavity length of 120 mm and a Nd:MgO:PPLN crystal. To achieve high single-pulse energy and high peak power in mid-infrared light sources, a LiNbO₃ electro-optic Q-switch (EOQ) is introduced for the first time in a mid-IR SOPO. A narrow-linewidth EOQ-SOPO rate equation is formulated, and experiments are conducted using a single Fabry-Pérot (F-P) etalon. At a 500 μs pump pulse width, a 4.71 mJ single pulse idler light at 3838.2 nm is achieved, with a linewidth of 0.412 nm, single-pulse width of 4.78 ns, and peak power of 985 kW. At 200 μs, the idler light at 3845.2 nm exhibits a minimum linewidth of 0.212 nm.