An optical parametric oscillator (OPO) based on magnesium-oxide-doped periodically poled lithium niobate (MgO:PPLN) is demonstrated to deliver visible femtosecond pulses, which were created through the intra-cavity nonlinear interactions within the PPLN itself. The signal from the OPO produces femtosecond pulses in the near-infrared region tunable from 1050 to 1600 nm. Visible femtosecond pulses in the range of 522-800 nm and those of 455-540 nm, respectively, were generated via second-harmonic generation (SHG) of signal photons and through sum-frequency generation (SFG) of pump and signal photons. Maximum output efficiencies of 9.2% at 614 nm and 8.0% at 522 nm for the SHG and SFG are attained, respectively, where the efficient visible pulse generation relies on the quasi-phase matching with the aid of the higher-order grating momentum.