Learned video coding (LVC) has recently achieved superior coding performance. In this paper, we model the rate-quality (R-Q) relationship for learned video coding by a parametric function. We learn a neural network, termed RQNet, to characterize the relationship between the bitrate and quality level according to video content and coding context. The predicted (R,Q) results are further integrated with those from previously coded frames using the least-squares method to determine the parameters of our R-Q model on-the-fly. Compared to the conventional approaches, our method accurately estimates the R-Q relationship, enabling the online adaptation of model parameters to enhance both flexibility and precision. Experimental results show that our R-Q model achieves significantly smaller bitrate deviations than the baseline method on commonly used datasets with minimal additional complexity.