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Unsupervised domain adaptation is one of the challenging problems in computer vision. This paper presents a novel approach to unsupervised domain adaptations based on the optimal transport-based distance. Our approach allows aligning target and source domains without the requirement of meaningful metrics across domains. In addition, the proposal can associate the correct mapping between source and target domains and guarantee a constraint of topology between source and target domains. The proposed method is evaluated on different datasets in various problems, i.e. (i) digit recognition on MNIST, MNIST-M, USPS datasets, (ii) Object recognition on Amazon, Webcam, DSLR, and VisDA datasets, (iii) Insect Recognition on the IP102 dataset. The experimental results show our proposed method consistently improves performance accuracy. Also, our framework can be incorporated with any other CNN frameworks within an end-to-end deep network design for recognition problems to improve their performance.