The 40-GHz rational harmonic mode-locking (RHML) and pulse-amplitude equalization of a semiconductor optical amplifier based fiber-ring laser (SOAFL) is demonstrated by the injection of a reshaped 10-GHz gain-switching FPLD pulse. A nonlinearly biased Mach-Zehnder modulator (MZM) is employed to detune the shape of the double-peak pulse before injecting the SOA, such that a pulse-amplitude equalized 4th-order RHML-SOAFL can be achieved by reshaping the SOA gain within one modulation period. An optical injection mode-locking model is constructed to simulate the compensation of uneven amplitudes between adjacent RHML pulse peaks before and after pulse-amplitude equalization. The indirect gain compensation technique greatly suppresses the clock amplitude jitter from 45% to 3.5% when achieving 4th-order RHML, and the amplitude fluctuation of sub-rational harmonic modulating envelope is attenuated by 45 dB. After pulse-amplitude equalization, the pulsewidth of the optical-injection RHML-SOAFL is 8 ps, which still obeys the trend predicted by the inverse square root of repetition rate. The phase noise contributed by the residual ASE noise of the RHML-SOAFL is significantly decreased from -84 to -90 dBc/Hz after initiating the pulse-amplitude equalization, corresponding to the timing jitter reduction from 0.5 to 0.28 ps.