In order to ensure the security of transmitted digital image effectively,an invertible chaotic 3D map based image encryption approach and its optimized algorithm are proposed based on the stretching and folding mechanisms of chaos.A gray-level image is depicted as a 3D matrix and mapped to a 2D image matrix according to proposed algorithm.Then,stretching and folding maps are used to permute the pixel positions of the 2D matrix.The stretching process is to transform the 2D image matrix to an array,and the folding process is to fold the array to another 2D image matrix with the same size as the original 2D matrix.Finally,the permuted 2D matrix is mapped back to a 3D matrix to obtain a cipher image.This proposed approach is invertible,it could be used for image encryption and decryption.The encryption and decryption algorithms are formulated,by which image encryption and decryption will do a large of calculation and consume a lot time for the image has large data quantity.In order to solve this problem,an optimized algorithm is proposed.Simulation results indicate that proposed optimized algorithm can increase image encryption speed,which is 3～4 times faster than that of the deduced formulas,proposed image encryption approach also can realize pixel permutation and substitution at the same time via one iteration map for the histogram information of the plain image,and can enhance the capability of resisting statistic attack.