Theoretical and experimental study is presented on grating period-tuned single-resonated quasi-phase-matched optical parametric oscillator (QPM-OPO) in multi-grating periodically poled lithium niobate (PPMgLN) pumped by 1064 nm laser. Theoretical analysis includes grating period tuning, pump threshold and converting efficiency. When pump power is 6.5 times of the pump threshold with Gauss beam pumping, a converting efficiency of 71% is obtained, however a converting efficiency of 100% may be obtained when pump power is (π/2)2 times of the pump threshold with plane wave pumping and phase matching. The pump beam polarization matches the e→e+e interaction in PPMgLN, thus maximal nonlinear coefficient d33 (27.4 pm/V) is effective. Widely mid-infrared wavelength tunable output from 2.7 μm to 4.8 μm has been obtained by grating period tuning. When pump power is 23 W with repetition rate of 7 kHz, an average output power of more than 3.2 W at 3.7 μm is obtained with slope efficiency of more than 18%, and 8 W at the corresponding idler wavelength of 1.49 μm and a corresponding converting efficiency of 63% are obtained. The experimental data are in agreement with numerical analysis results.