A 1020 nm fiber laser is designed based on fiber Bragg grating and then its output power is boosted to 590 mW through a two-stage amplifier. A tandem pumping fiber amplifier is constructed with the 1020 nm laser used as a pump source. The output power and the efficiency of the amplifier are measured with different lengths of gain fiber. A 385 mW maximum output power with an 81% slope-efficiency is achieved when the gain fiber is 8.5 m. The output power and the efficiency of a traditional amplifier in which 976 nm diode laser is used as a pump source are also measured. The experimental results indicate that tandem pumping fiber amplifier can achieve a higher efficiency than traditional fiber amplifier.