Smart grids incorporating internet-of-things are emerging solutions to provide a reliable, sustainable and efficient electricity supply, and electric vehicle drivers can access efficient charging services in the smart grid. However, traditional electric vehicle charging systems are vulnerable to distributed denial of service and privileged insider attacks when the central charging server is attacked. The blockchain-based charging systems have been proposed to resolve these problems. In 2018, Huang et al. proposed the electric vehicle charging system using lightning network and smart contract. However, their system has an inefficient charging mechanism and does not guarantee security of key. We propose a secure charging system for electric vehicles based on blockchain to resolve these security flaws. Our charging system ensures the security of key, secure mutual authentication, anonymity, and perfect forward secrecy, and also provides efficient charging. We demonstrate that our proposed system provides secure mutual authentication using Burrows-Abadi-Needham logic and prevents replay and man-in-the-middle attacks using automated validation of internet security protocols and applications simulation tool. Furthermore, we compare computation and communication costs with previous schemes. Therefore, the proposed charging system efficiently applies to practical charging systems for electric vehicles.