In the state-of-the-art video coding standard-High Efficiency Video Coding (HEVC), context-adaptive binary arithmetic coding (CABAC) is adopted as the entropy coding tool. In CABAC, the binarization processes are manually designed, and the context models are empirically crafted, both of which incur that the probability distribution of the syntax elements may not be estimated accurately, and restrict the coding efficiency. In this paper, we adopt a convolutional neural network-based arithmetic coding (CNNAC) strategy, and conduct studies on the coding of the DC coefficients for HEVC intra coding. Instead of manually designing binarization process and context model, we propose to directly estimate the probability distribution of the value of the DC coefficient using densely connected convolutional networks. The estimated probability together with the real DC coefficient are then input into a multi-level arithmetic codec to fulfill entropy coding. Simulation results show that our proposed CNNAC leads to on average 22.47% bits saving compared with CABAC for the bits of DC coefficients, which corresponds to 1.6% BD-rate reduction than the HEVC anchor.