Electric vehicle (EV) is becoming more and more popular in our daily life, which replaces the traditional fuel vehicles to reduce carbon emissions and protect the environment. The EVs need to be charged, but the number of charging piles in a charging station (CS) is limited and charging is usually more time-consuming than fueling. According to this scenario, we propose a secure and efficient charging scheduling system based on DAG-blockchain and double auction mechanism. In a smart area, it attempts to assign EVs to the available CSs in the light of their submitted charging requests and status information. First, we design a lightweight charging scheduling framework that integrates DAG-blockchain and modern cryptography technology to ensure security and scalability during performing scheduling and completing tradings. In this process, a constrained double auction problem is formulated because of the limited charging resources in a CS, which motivates the EVs and CSs in this area to participate in the market based on their preferences and statuses. Due to this constraint, our problem is more complicated and harder to achieve the truthfulness as well as system efficiency compared to the existing double auction model. To adapt to it, we propose two algorithms, namely the truthful mechanism for charging (TMC) and efficient mechanism for charging (EMC), to determine the assignments between EVs and CSs and pricing strategies. Then, both theoretical analysis and numerical simulations show the correctness and effectiveness of our proposed algorithms.