Using the generalized nonlinear Schrödinger equation, we present a numerical study of trapping of dispersive waves by solitons during femtosecond pumped supercontinuum generation in photonic crystal fiber with single or double zero dispersive wavelength. Numerical simulation results show that the generated supercontinuum in photonic crystal fiber with two zero dispersive wavelengths includes both blue-shifted dispersive wave (B-DW) and red-shifted dispersive wave (R-DW) while the generated supercontinuum in photonic crystal fiber with single zero dispersive wavelength has only blue-shifted dispersive wave. We find a novel phenomenon that not only B-DW but also R-DW can be trapped by solitions via four-wave mixing when the group-velocity matching between the soliton and the dispersive wave is satisfied, thus leading to the generation of new spectral components. In order to clearly display the evolution of soliton trapping of dispersive waves, the spectrogram of output pulses is observed using cross-correlation frequency-resolved optical gating technique.