We have studied the magnetic and electrical transport properties of epitaxial NiAs-type CrTe thin films grown on SrTiO₃(111) substrates. Unlike rectangle hysteresis loops obtained from magnetic measurements, we have identified intriguing extra bump/dip features from anomalous Hall experiments on the films with thicknesses less than 12 nm. This observed Hall anomaly is phenomenologically consistent with the occurrence of a topological Hall effect(THE) in chiral magnets with a skyrmion phase. Furthermore, the THE contribution can be tuned by the film thickness, showing the key contribution of asymmetric interfaces in stabilizing Néel-type skyrmions. Our work demonstrates that a CrTe thin film on SrTiO₃(111) substrates is a good material candidate for studying real-space topological transport.