This work presents a numerical investigation of the self-steepening (SS) effect on the soliton spectral tunneling (SST) effect in a photonic crystal fiber (PCF) with three zero dispersion wavelengths. Interestingly, the spectral range and flatness can be flexibly tuned by adjusting the SS value. When the SS coefficient increases, the energy between solitons and dispersion waves is redistributed, and the red-shifted soliton forms earlier in the region of long wavelength anomalous dispersion. As a consequence, the SST becomes more obvious. The findings of this work provide interesting insights in regard to the impact of the SST effect on tailored supercontinuum generation.