A pulsed laser for laser guide stars with a 100 MHz repetition rate and 1 ns pulse width was achieved by external modulation of a continuous wave (CW) laser with a 70 kHz spectrum width. The laser is amplified first by two fiber pre-amplifiers and then by four solid-state power amplifiers. The laser achieves gains as high as 36 dB in the fiber pre-amplifiers due to the long gain medium length. The output power from the fiber amplifiers is 2.1 W. The laser receives further amplification in the solid-state amplifiers and retains good beam quality by aberration compensation. The final output average power is 102.9 W, and the beam quality factor M² is 1.46. The laser reaches high power without spectrum width and pulse width broadening at the 100 MHz repetition rate. The spectrum width of the pulsed laser is less than 0.8 GHz, which is close to the Fourier transform limit. Such a laser with single-frequency, high-repetition, and high-power features along with good beam quality will be valuable for many research areas.