We present a first application of the subhalo abundance matching (SHAM) method to describe the redshift-space clustering of galaxies including the non-linear redshift-space distortion, i.e., the Fingers-of-God. We find that the standard SHAM connecting the luminosity of galaxies to the maximum circular velocity of subhalos well reproduces the luminosity dependence of redshift-space clustering of galaxies in the Sloan Digital Sky Survey in a wide range of scales from 0.3 to 40 Mpc/h. The result indicates that the SHAM approach is very promising for establishing a theoretical model of redshift-space galaxy clustering without additional parameters. We also test color abundance matching using two different proxies for colors: subhalo age and local dark matter density following the method by Masaki et al. (2013b). Observed clustering of red galaxies exhibits much stronger Fingers-of-God effect than blue galaxies. We find that the subhalo age model describes the observed color-dependent redshift-space clustering much better than the local dark matter density model. The result infers that the age of subhalos is a key ingredient to determine the color of galaxies.