In Symmetric cryptography both the sender and receiver agree with the same key before they start communicating secretly. Same key is used for encryption and decryption. The communication is secret as long as the key is kept secret. A desirable property of symmetric encryption is termed as avalanche effect by which two different keys produces different ciphertext for the same message. Essential properties of chaos functions are sensitivity to initial conditions and ergodicity, which makes two nearby keys to generate different cipher texts. Sensitivity to initial conditions property of chaos can be exploited to produce avalanche effect. We propose a symmetric encryption algorithm which uses logistic map. We show that the keys with negligible difference generate different cipher texts. Cryptanalysis of the proposed algorithm shows that it is resistant to various attacks and stronger than existing encryption algorithms.