We have extended the contour-path effective-permittivity (CP-EP) finite-difference time-domain (FDTD) algorithm by A. Mohammadi et al., Opt. Express 13, 10367 (2005), to linear dispersive materials using the Z-transform formalism. We test our method against staircasing and the exact solution for plasmon spectra of metal nanoparticles. We show that the dispersive contour-path (DCP) approach yields better results than staircasing, especially for the cancellation of spurious resonances.