In almost all video applications, a video rate control algorithm (RCA) is used by the encoder. The RCA tunes the quantization parameter (QP) to match the encoded bit rate to the available capacity of the communication channel or storage media. Conventional RCAs usually utilize a rate-quantization (R-Q) or a rate-distortion (R-D) model for rate control. A content-based R-Q model for intra coding tree units (CTUs) of the high-efficiency video coding standard is proposed. The model is a convolutional neural network that observes pixels of a CTU and its intraprediction reference pixels and it estimates required bit counts for intracoding the CTU for all QP values simultaneously. The proposed model can be easily used by any video RCA. A given RCA just selects a proper QP for which the estimated bit counts are closer to the allocated bit budget. The evaluation results show a high accuracy for the model. According to simulation results, the mean absolute normalized bit error at CTU level is 19.66% and it decreases to 6.85% at the frame level. Compared with similar networks, the proposed structure has a very low computational complexity.