With the development of the internet and social networks, the multimedia data, particularly digital Images, has been of increasing interest to scientists. Due to their advantages including high speed, high security, and complexity, chaotic functions have been broadly employed in Image encryption. The present paper proposed a modified logistic map function which resulted in higher scattering in the obtained results. Confusion and diffusion functions, as the two main actions in cryptography, are not necessarily performed in order, i. e. each of these two functions can be applied on the Image in either order, provided that the sum of total functions does not exceed 10. So, to calculate the sum of functions, confusion has the factor of 1 and diffusion has the factor of 2. To simulate this method, a binary stack was used. Application of binary stack and pseudo-random numbers obtained from the modified chaotic function increased the complexity of the proposed encryption algorithm. The security key length, entropy value, NPCR and UACI values, and correlation coefficient represented in the analytical results revealed the capability and validity of the proposed method. Analyzing the obtained results and comparing the algorithm to other investigated methods clearly verified high efficiency of the proposed method.