This study investigates top-of-atmosphere (TOA) radiation budget (Rt) and cloud radiative effects (CREs) over the Tibetan Plateau (TP) and adjacent Asian monsoon regions including Eastern China (EC) and South Asia (SA) using the Coupled Model Intercomparison Project 6 (CMIP6) simulations. Considerable simulation biases occur but specific causes differ over these regions. Over the TP, most models underestimate the intensity of annual mean Rt and cloud radiative cooling effect, and they are hard to capture the Rt over the TP during the cold-warm transition period with the largest model uncertainty. The biases in surface air temperature and cloud fractions contribute to cloud-radiation biases over the western and eastern TP, respectively. Over EC, the intensity of Rt and cloud radiative cooling effect is seriously underestimated especially in the springtime when the model spread is large, and their biases are closely related to less low-middle cloud fractions and weaker ascending motion. Over SA, simulation biases mainly arise from longwave radiative components associated with less high cloud fraction and weaker convection, with the large model spread in the summertime. The annual cycles of Rt and CREs over EC and SA can be well reproduced by most models while the summertime peak of net CRE over the TP is later than the observation. The Rt and its simulation bias strongly depend on cloud radiative cooling effect over EC, SA, and the eastern TP. Our results demonstrate that contemporary climate models still have obvious difficulties in representing complex and various cloud-radiation processes in Asian monsoon regions.