Feistel and SPN are the two main structures in a block cipher. Feistel is a symmetric structure which has the same structure in encryption and decryption, but SPN is not a symmetric structure. In this paper, we propose a SPN block cipher so called SSB which has a symmetric structure in encryption and decryption. The proposed SSB is composed of the even numbers of N rounds. Each round consists of a round key addition layer, a subsitution layer, a byte exchange layer and a diffusion layer. The subsitution layer of the odd round is inverse function of one of the even round. And the diffusion layer is a MDS involution matrix. The differential and linear attack probability of SSB is $2^{-306}$ which is same with AES. The proposed symmetric SPN block cipher SSB is believed to construct a safe and efficient cipher in Smart Card and RFID environments which is in limited hardware and software resources.