We present the first Doppler images of the active eclipsing binary system SZ Psc, based on the high-resolution spectral data sets obtained in 2004 November and 2006 September--December. The least-squares deconvolution technique was applied to derive high signal-to-noise profiles from the observed spectra of SZ Psc. Absorption features contributed by a third component of the system were detected in the LSD profiles at all observed phases. We estimated the mass and period of the third component to be about $0.9 M_{odot}$ and $1283 pm 10$ d, respectively. After removing the contribution of the third body from the LSD profiles, we derived the surface maps of SZ Psc. The resulting Doppler images indicate significant starspot activities on the surface of the K subgiant component. The distributions of starspots are more complex than that revealed by previous photometric studies. The cooler K component exhibited pronounced high-latitude spots as well as numerous low- and intermediate-latitude spot groups during the entire observing seasons, but did not show any large, stable polar cap, different from many other active RS CVn-type binaries.