Recently an image encryption algorithm based on DNA encoding and the Elliptic Curve Cryptography (ECC) is proposed. This paper aims to investigate the security the DNA-based image encryption algorithm and its resistance against chosen plaintext attack. The results of the analysis demonstrate that security of the algorithm mainly relies on one static shuffling step, with a simple confusion operation. In this study, a practical plain image recovery method is proposed, and it is shown that the images encrypted with the same key could easily be recovered using the suggested cryptanalysis method with as low as two chosen plain images. Also, a strategy to improve the security of the algorithm is presented in this paper.