Cellular Automaton is an idealized parallel processing machine which is an array (1-D, 2-D) of numbers or symbols called cell values together with an updating rule. A cell value is updated based on this updating rule, which involves the cell value as well as other cell values in a particular neighborhood. A fundamental objective of cryptography is to enable two people to communicate over an insecure channel (a public channel such as internet) in such a way that any other person is unable to recover their message (called the plaintext) from what is sent in its place over the channel (the cipher text). The transformation of the plaintext into the cipher text is called encryption, or enciphering. The transformation of the cipher text into the plaintext is called decryption, or deciphering. In this paper we present a new encryption and decryption algorithm based on the linear (periodic boundary-PB) and nonlinear Cellular Automata rules. First we apply PB CA rules to plain text and key. The result of both plain text and key is XORed. Then the result of XOR operation is fed to substitution box( S-box) and again PB CA rules are applied for exchange and shift operations. At the end Complement operation is applied for encryption of plain text. The decryption process is carried out just similar to encryption but in the reverse way. Both the process of encryption and decryption is performed for 8 numbers of rounds in order to avoid the dependency between the plain text and cipher text.