Although significant progress in automatic learning of steganographic cost has been achieved recently, existing methods designed for spatial images are not well applicable to JPEG images which are more common media in daily life. The difficulties of migration mostly lie in the unique and complicated JPEG characteristics caused by 8x8 DCT mode structure. To address the issue, in this paper we extend an existing automatic cost learning scheme to JPEG, where the proposed scheme called JEC-RL (JPEG Embedding Cost with Reinforcement Learning) is explicitly designed to tailor the JPEG DCT structure. It works with the embedding action sampling mechanism under reinforcement learning, where a policy network learns the optimal embedding policies via maximizing the rewards provided by an environment network. The policy network is constructed following a domain-transition design paradigm, where three modules including pixel-level texture complexity evaluation, DCT feature extraction, and mode-wise rearrangement, are proposed. These modules operate in serial, gradually extracting useful features from a decompressed JPEG image and converting them into embedding policies for DCT elements, while considering JPEG characteristics including inter-block and intra-block correlations simultaneously. The environment network is designed in a gradient-oriented way to provide stable reward values by using a wide architecture equipped with a fixed preprocessing layer with 8x8 DCT basis filters. Extensive experiments and ablation studies demonstrate that the proposed method can achieve good security performance for JPEG images against both advanced feature based and modern CNN based steganalyzers.