We present an efficient and tunable source generating multi-watt single-frequency red radiation by intra-cavity frequency doubling of the signal in a MgO-doped periodically poled LiNbO3 (MgO:PPLN)-based singly resonant optical parametric oscillator (SRO). By optimally designing the SRO cavity in a six-mirror configuration, we generate ≈276 nm tunable idler radiation in mid-infrared with a maximum power of Pi=2.05 W at a pump power of Pp=14.0 W. The resonant signal is frequency doubled using a 10 mm-long BiB3O6 (BiBO) crystal which resulted in tunability of a red beam from ≈753 to 780 nm band with maximum power Pr≈4.0 W recorded at λr≈756 nm. The deployment of a six-mirror SRO ensures single-frequency generation of red across the entire tuning range by inducing additional losses to Raman modes of LiNbO3 and, thus, inhibiting their oscillation. Using a scanning Fabry-Perot interferometer (FPI), nominal linewidth of the red beam is measured to ≈3 MHz which changes marginally over the entire tuning range. Long-term (over 1 h) peak-to-peak frequency fluctuation of the generated red beam is estimated to be about 3.3 GHz under free-running conditions at Pp=14.0 W. The generated red beam is delivered in a TEM00 mode profile with M2≤1.32 at maximum power in a red beam.