We present a new method of SBS suppression in fiber amplifier system by employing simultaneously phase and intensity modulation. In this way, a GHz narrow-linewidth polarization-maintaining (PM) all-fiber pulsed laser is obtained based on a master oscillator power amplifier (MOPA) configuration. The pulsed seed is generated from a single-frequency continuous wave (CW) laser at 1064 nm by simultaneous modulation using an electro-optic intensity modulator (EOIM) and an electro-optic phase modulator (EOPM). Theoretical model is built and simulation framework has been established to estimate the SBS threshold of the pulsed amplifier system before and after modulation. In experiment, in order to suppress SBS effectively, the pulse width is set to be 4 ns and the phase modulation voltage is set to be 5 V. After amplifying by the amplifier chain, a ~3.5 ns pulsed laser with average/peak power of 293 W/3.9 kW is obtained at intensity repetition rate of 20 MHz and phase repetition rate of 100MHz, showing good agreement with simulation results. The linewidth of the output laser is ~4.5 GHz, the M(2) factor at maximal output power is measured to be ~1.1 and the slope efficiency is ~86%.This method provides some references to suppress the SBS in narrow linewidth pulsed amplifier systems.