We propose a simple and effective synchronization technique between a reference electrical oscillator and a mode-locked laser for a narrowband picosecond Laser-Compton scattering γ-ray source by using a commercial-based 1-chip frequency synthesizer, which is widely used in radio communication. The mode-locked laser has been successfully synchronized in time with a jitter of 180 fs RMS for 10 Hz-100 kHz bandwidth. A good stability of 640 μHz at 80 MHz repetition rate for 10 h operation has also been confirmed. We discuss in detail the design and performance of this technique (in terms of timing jitter, stability, and validity).