Continuous-wave operation of a mode-locked optical parametric oscillator has been achieved with the use of an all-solid-state laser pump. The oscillator, based on a 5-mm-long KTP crystal, is synchronously pumped at 523.5 nm by a continuous train of picosecond pulses at 352 MHz obtained by frequency doubling the output of a cw mode-locked, diode-laser-pumped Nd:YLF laser in an external enhancement cavity. The doubly resonant oscillator has a pump power threshold of 150 mW, corresponding to a peak mode-locked pumping intensity of 4 MW/cm2. At 3.8 times above threshold, the oscillator converts -7% of the pump power into externally usable signal and idler outputs at 1.020 and 1.075-mu-m. The performance of the oscillator may be enhanced significantly through optimization of the design parameters.