The microwave complex surface impedance Zs of Y(Ni1−xPtx)2B2C was measured at 0.5 K under magnetic fields H up to 7 T. In nominally pure YNi2B2C, which is a strongly anisotropic s-wave superconductor, the flux flow resistivity ρ f calculated from Zs was twice as large as that expected from the conventional normal-state vortex core model. In Pt-doped samples where the gap anisotropy is smeared out, the enhancement of ρ f is reduced and ρ f approaches to the conventional behavior. These results indicate that energy dissipation in the vortex core is strongly affected by the anisotropy of the superconducting gap.