Context : Aims : We investigate the surface spot activity of the rapidly rotating , lithium-rich active single K-giant DI Psc to measure the surface differential rotation and understand the mechanisms behind the Li-enrichment . Methods : Doppler imaging was applied to recover the surface temperature distribution of DI Psc in two subsequent rotational cycles using the individual mapping lines Ca i 6439 , Fe i 6430 , Fe i 6421 and Li i 6708 . Surface differential rotation was derived by cross-correlation of the subsequent maps . Difference maps are produced to study the uniformity of Li-enrichment on the surface . These maps are compared with the rotational modulation of the Li i 6708 line equivalent width . Results : Doppler images obtained for the Ca and Fe mapping lines agree well and reveal strong polar spottedness , as well as cool features at lower latitudes . Cross-correlating the consecutive maps yields antisolar differential rotation with shear coefficient \alpha = -0.083 \pm 0.021 . The difference of the average and the Li maps indicates that the lithium abundance is non-activity related . There is also a significant rotational modulation of the Li equivalent width . Conclusions :