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In this paper, a novel Extended Logistic Chaotic Map (ELCM) with two control parameters is proposed. Overcoming the major drawback of the standard Logistic and other existing chaotic maps, the ELCM not only has infinite chaotic range as well as good ergodicity, but also has a simple structure just like the Logistic map, which greatly facilitates its practical implementation and becomes very suitable for today's real-time applications. Moreover, a new color image encryption scheme based on chaos concept, DNA (Deoxyribonucleic Acid) encoding and Convolutional Neural Network (CNN) is also presented. To perform a chaotic scrambling, the ELCM is however used at different stages of the encryption process. In addition, a pre-trained AlexNet CNN is used to generate a public key. After XORing with the secret key, the latter is used, on the one hand, to generate the initials values and the control parameters of the ELCM. On the other hand, it will be split into two keys in order to generate a random grayscale image, which will then be XORed with the three components (i.e., R, G and B) of the color plaintext image. Afterward, a permutation operation, DNA encoding, diffusion operation as well as bit reversion operation are then applied to the R, G and B components. The performance evaluation demonstrates that the ELCM not only has an infinite chaotic parameter range, but also exhibits a high chaotic complexity. Besides, experimental results as well as security analysis confirm that with NPCR of 99.6287%, the designed color image encryption scheme achieves an average entropy of 7.9975 and a near zero correlation (-0.0027). Furthermore, the proposed encryption scheme is in fact of higher security level in comparison to other schemes recently presented in the literature, thus making it highly suitable for today's real-time applications. [ABSTRACT FROM AUTHOR]