In order to solve the problem of task offloading with dependent subtasks in mobile edge computing (MEC), we propose a graph mapping offloading model based on deep reinforcement learning (DRL). We model the user's computing task as directed acyclic graph (DAG), called DAG task. Then the DAG task is converted into a topological sequence composed of task vectors according to the custom priority. And the model we proposed can map the topological sequence to offloading decisions. The offloading problem is formulated as a Markov decision process (MDP) to minimize the trade-off between latency and energy consumption. The evaluation results demonstrate that our DRL-based graph mapping offloading model has better decision-making ability, which proves the availability and effectiveness of the model.