We investigate the effect of a symmetric gap surface plasmon polariton (SPP) waveguide on ultrashort pulses with a central wavelength of 850 nm and a width of 20 fs using the finite-difference time-domain method. The length of the waveguide is 560 nm. Linear and nonlinear dielectrics are chosen to be the core layers whose thicknesses are set to be 20, 50, 100 and 200 nm, respectively. The results show that for the linear case, strong coupling of the SPP mode can lead to the pulse tailing phenomenon and spectrum compression due to waveguide resonance. For the nonlinear case, the output pulse is broadened and the fluctuation is more complex than the input pulse and can induce the spectrum splitting as well. The smaller the thickness of the core layer is, the more distinct the pulse distortion is, which may be due to the combined effects of dispersion, waveguide resonance and self-phase modulation.