Mobile edge computing (MEC) technology guarantees the privacy and security of large-scale data in the Narrowband-IoT (NB-IoT) by deploying MEC servers near base stations to provide sufficient computing, storage, and data processing capacity to meet the delay and energy consumption requirements of NB-IoT terminal equipment. For the NB-IoT MEC system, this paper proposes a resource allocation algorithm based on deep reinforcement learning to optimize the total cost of task offloading and execution. Since the formulated problem is a mixed-integer non-linear programming (MINLP), we cast our problem as a multi-agent distributed deep reinforcement learning (DRL) problem and address it using dueling Q-learning network algorithm. Simulation results show that compared with the deep Q-learning network and the all-local cost and all-offload cost algorithms, the proposed algorithm can effectively guarantee the success rates of task offloading and execution. In addition, when the execution task volume is 200KBit, the total system cost of the proposed algorithm can be reduced by at least 1.3%, and when the execution task volume is 600KBit, the total cost of system execution tasks can be reduced by 16.7% at most.