Blockchain, which has a distributed structure, has been widely used in many areas. Especially in the area of smart cities, blockchain technology shows great potential. The security issues of blockchain affect the construction of smart cities to varying degrees. With the rapid development of quantum computation, elliptic curves cryptosystems used in blockchain are not secure enough. This paper presents a blockchain system based on lattice cipher, which can resist the attack of quantum computation. The most challenge is that the size of public keys and signatures used by lattice cryptosystems is typically very large. As a result, each block in a blockchain can only accommodate a small number of transactions. It will affect the running speed and performance of the blockchain. For overcoming this problem, we proposed a way that we only put the hash values of public keys and signatures on the blockchain and store the complete content of them on an IPFS (interplanetary file system). In this way, the number of bytes occupied by each transaction is greatly reduced. We design a bitcoin exchange scheme to evaluate the performance of the proposed quantum-resistant blockchain system. The simulation platform is verified to be available and effective.