Magnetic materials hosting topological spin textures such as magnetic skyrmions exhibit a nontrivial Hall effect, namely, a topological Hall effect (THE). In this study, we demonstrate the emergence of THE in thin films of half-metallic perovskite manganites. To stabilize magnetic skyrmions, we control the perpendicular magnetic anisotropy by imposing a compressive epitaxial strain as well as by doping with a small amount of Ru. When the perpendicular magnetic anisotropy is tuned so that it is balanced with the magnetic dipolar interaction, the film exhibits a sizable THE in a magnetization reversal process. Real-space observations indicate the formation of skyrmions, some having a high topological charge number. The present result opens up the possibility of novel functionalities that emerge under keen competition between the skyrmion phase and other rich phases of perovskite manganites with various orders in spin, charge, and orbital degrees of freedom.