In this paper, we present a frame-level constant bit-rate (CBR) control method using recursive Bayesian estimation (RBE) for Versatile Video Coding (VVC). An R-lambda model for rate control (RC) has handled the total texture and non-texture bits at a time and has worked reasonably well in High Efficiency Video Coding (HEVC). Nevertheless, if the rate estimation is inaccurately performed, that is, the R and lambda values for a current frame cannot be linearly modeled with their respective values in the previous frames, the resulting RC performance is degraded. In our work, we adopt the RBE which alternates prediction and update steps not only to precisely estimate the rates, but also to allocate target bits based on the changes in the distortions of the previously coded frames, thus considering the rates and distortions simultaneously. Therefore, an elaborate RC can be performed especially at fluctuating frame complexities. Experimental results show that our RC method outperforms the RC of VVC Test Model (VTM-5.0) in terms of normalized root mean square error (NRMSE) with maximum (average) 34.95% (12.35%) improvement, and maintains higher visual quality consistency in terms of standard deviation of PSNR by 33.07% (22.34%) improvement for All Intra (AI), maximum (average) 44.82% (27.29%) and 22.54% (9.50%) for Low Delay (LD), and maximum (average) 47.35% (39.94%) and 30.35% (18.54%) for Random Access (RA), respectively, compared to the default RC method of the original VTM-5.0.