Satellite observations clearly reveal that superthermal electrons in space plasma generally possess a pronounced non-Maxwellian distribution that can be well modeled by a distribution. In this paper, one-dimensional (1-D) particle-in-cell simulations are performed to investigate the evolution of whistler waves driven by superthermal electrons with a typical distribution in the presence of a cold plasma population. The results obtained from the linear theory are first confirmed: with the increase of the spectral index for the distribution, the linear growth rate of the excited waves increases and instability threshold for the temperature anisotropy (A = T /T − 1) decreases. Then we further find that with the increase of , the fluctuating magnetic field energy density at the saturation stage also increases. Therefore, from both the linear growth rate and the fluctuating magnetic field energy density at the saturation stage, we can find that a bi-Maxwellian distribution ( → ) overestimates the importance of whistler waves, since the observed value of lies in the range 2 ≤ ≤ 6. We also find that the values of the electron distributions become smaller with the excitation of the whistler waves.