In this paper, an image encryption system is proposed that uses only addition operation to achieve higher efficiency at diffusion phase after DNA encoding at pixel level. The image is first permuted and then encoded into DNA bases using sub-set of DNA complementary rules chaotically. Afterwards, the adjacent columns of DNA encoded image are added in the substitution phase named as inter-intra pixels substitution which followed by row addition named as inter-pixels substitution. This substitution is performed by adding DNA bases where each DNA base is composed of 2-bits. The addition operation performs randomly between DNA bases named mixed inter-intra pixel substitution. To strengthen security, initial conditions for chaotic maps are computed from SHA-256 hash of plain image which leads to enhance the resistance against known/chosen-plaintext and differential attacks. Due to fewer computational operations, the efficiency of the proposed cipher is high. The simulated results show that the proposed technique is extremely robust against statistical and differential attacks. It successfully surpassed the statistical tests such as Histogram, Correlation, Chi-Square and Entropy. For differential attack, it passed quantitative as well as qualitative Number of Pixel Change Rate (NPCR) and Unified Average Cipher Intensity (UACI) tests in a single round of encryption.