Advanced image encryption schemes for secure transmission and storage are increasingly needed for a number of applications like medical, military, satellite etc. In this paper, a novel image encryption algorithm based on Logistic and Tinkerbell map is proposed.The proposed method uses two 1-D Logistic maps with different keys and one 2-D Tinkerbell map. The chaotic sequence generated is mixed sequence from the and sequences of Tinkerbell map depending on the chaotic sequences of two logistic maps. The main advantage of such a scheme is complex chaotic behavior of the generated chaotic sequences. The security and performance of the proposed method is analyzed thoroughly by using key-sensitivity, keyspace, statistical, entropy, differential and performance analysis. The proposed approach achieves the required level of security with only one round of encryption operation. Hence the proposed method is computationally efficient.