The design, optimization, and performance of a narrow-bandwidth high-repetition-rate singly resonant picosecond optical parametric oscillator, based on a noncritical phase-matched lithium triborate crystal and synchronously pumped by the second harmonic of a mode-locked Nd:YLF laser, is described. The spectral bandwidth of the signal output is reduced with an intracavity birefringent filter to 0.06 nm. Furthermore, the filter allowed fast scanning of the output wavelength within the phase-matching bandwidth. A maximum average signal output of 1.6 W in pulses with a duration of 22 ps was obtained when the optical parametric oscillator was pumped four times above threshold with a 4-W pump source. With the present mirror set the signal and the idler wavelengths were tunable from, respectively, 740 to 930 nm and 1220 to 1830 nm. The total external power conversion efficiency was better than 55%.