High-precision transit photometry supplies ideal opportunities for detecting new exoplanets and characterizing their physical properties, which usually encode valuable information for unveiling the planetary structure, atmosphere, and dynamical history. We present revised properties of three transiting systems (i.e. HAT-P-13, HAT-P-16, and WASP-32) through analyzing TESS photometry and ground-based transit observations, which were obtained at the 1-m and 2.4-m telescopes of Yunnan Observatories, China, and the 1.2-m telescope of Hamburg Observatory, Germany, as well as the data in the literature. During modelling the transit light curves, Gaussian process is employed to account for the potential systematic errors. Through comprehensive timing analysis, we find that both HAT-P-13b and HAT-P-16b show significant timing variations (TTVs) that can be explained by apsidal precession. TTVs of WASP-32b may be led by a decaying orbit due to tidal dissipation or apsidal precession. However, the current observations can not rule out the origins of three systems' TTVs from gravitational perturbations of close planetary companions conclusively.