We report a high-repetition-rate, singly resonant optical parametric oscillator based on the nonlinear crystal LiB3O5, which is synchronously pumped by a continuous train of picosecond pulses from a self-mode-locked Ti:sapphire laser. Under temperature-tuned noncritical type I phase matching, total average near-infrared output powers of 90 mW at a repetition rate of 81 MHz have been generated over a signal (idler) tuning range of 1.374-1.530 mum (1.676-1.828 mum). Without dispersion compensation, transform-limited signal pulses with durations of 520-780 fs have been obtained at 1.2 times threshold for 1.8-ps input pump pulses.