Since HEVC intra rate control has no prior information to rely on for coding, it is a difficult work to obtain the optimal λ for every coding tree unit (CTU). In this paper, a convolutional neural network (CNN) based intra rate control is proposed. Firstly, a CNN with two last output channels is used to predict the key parameters of the CTU R-λ curve. For well training the CNN, a combining loss function is built and the balance factor γ is explored to achieve the minimum loss result. Secondly, the initial CTU λ can be calculated by the predicted results of the CNN and the allocated bit per pixel (bpp). According to the rate distortion optimization (RDO) of a frame, a spatial equation is derived between the CTU λ and the frame λ. Lastly, The CTU clipping function is used to obtain the optimal CTU λ for the intra rate control. The experimental results show that the proposed algorithm improves the intra rate control performance significantly with a good rate control accuracy.