The microwave complex surface impedance Z_s of Y(Ni_{1-x}Pt_x)_2B_2C was measured at 0.5 K under magnetic fields H up to 7T. In nominally pure YNi_2B_2C, which is a strongly anisotropic s-wave superconductor, the flux flow resistivity rho_f calculated from Z_s 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 rho_f is reduced and rho_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.
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