Fiber laser system in master oscillator power amplifier (MOPA) scheme is a promising technique for high-power narrow-linewidth laser output. With modulation-generated pulsed seed laser, the fiber MOPA benefits the flexible temporal behavior. However, the spectral linewidth broadening induced by self-phase modulation (SPM) is the main obstacle to achieving high-power single-frequency laser output with narrow spectral linewidth, especially for pulsed fiber MOPA in which the kilowatts level peak power results in strong nonlinearity. The SPM induced linewidth broadening is related to the derivative of light intensity with respect to time (d I/d t). Theoretically, if the d I/d tof the laser pulse is a constant, the SPM process will not generate any new frequency components. Hence, the linewidth broadening can be suppressed. In this work, we demonstrate a high-power single-frequency Yb fiber amplifier at 1064 nm, in which a sawtooth laser pulse is employed to suppress the SPM induced linewidth broadening, for obtaining the output with near-transform-limited narrow linewidth. The sawtooth-shaped seed pulse train is generated through using an electro-optic intensity modulator to modulate the continuous-wave (CW) output of a single-frequency fiber laser. After being pre-amplified, the seed laser with a pulse repetition rate of 20 kHz is coupled into the main amplifier, in which a piece of 0.9-m-long Yb-doped silica fiber with core and clad diameters of 35 μm and 250 μm, respectively, is used as a gain medium. The seed laser is enhanced to an average power value of 3.13 W under a launched 976-nm pump power value of 11.3 W before the onset of stimulate Brillouin scattering. The pulse energy 157 μJ and the pulse width 6.5 ns give a peak power of 24 kW. The spectral linewidth measured using a scanning Fabry-Perot interferometer at the maximum power is only 83 MHz, which is quite close to the 76-MHz transform-limited linewidth of the 6.5-ns sawtooth-shaped pulse. For comparison, we also conduct an experiment with a common Gaussian-shaped seed laser, in which the spectral linewidth is broadened significantly with a peak power value of only 1.5 kW. The results here reveal that the using of the sawtooth-shaped pulse is a promising technique to suppress the SPM induced spectral linewidth broadening in high-peak-power fiber amplifiers and acquire near-transform-limited narrow-linewidth laser output.