The experimental study on the random characteristic of chaotic laser in the amplification process is carried out. A ring cavity structure is usually applied to generate chaotic laser based on the nonlinear Kerr effect in fiber. The outputs of chaotic laser with different powers are realized by controlling pump current, and they are amplified by ytterbium-doped fiber amplifier. Then, the random characteristic of chaotic laser in the amplification process is analyzed quantitatively by permutation entropy, skewness and kurtosis. The results show that the permutation entropy decreases with the increase of the pump current of the fiber amplifier and tends to a stable value. The skewness and kurtosis first increase and then decrease with the increase of the pump current of the fiber amplifier when the permutation entropy is similar, indicating that the random characteristic of the chaotic laser first decreases and then increases during the amplification process.