Nowadays, society is growing and crowded, the construction of automatic smart waste sorter machine utilizing the intelligent sensors is important and necessary. To build this system, trash classification from trash images is an important issue in computer vision to be addressed for integrating into sensors. Therefore, this study proposes a robust model using deep neural networks to classify trash automatically which can be applied in smart waste sorter machines. Firstly, we collect the VN-trash dataset that consists of 5904 images belonging to three different classes including Organic, Inorganic and Medical wastes from Vietnam. Next, this study develops a deep neural network model for trash classification named DNN-TC which is an improvement of ResNext model to improve the predictive performance. Finally, the experiments are conducted to compare the performances of DNN-TC and the state-of-the-art methods for trash classification on VN-trash dataset as well as Trashnet dataset to show the effectiveness of the proposed model. The experimental results indicate that DNN-TC yields 94% and 98% in terms of accuracy for Trashnet and VN-trash datasets respectively and thus it outperforms the state-of-the-art methods for trash classification on both experimental datasets. INDEX TERMS Trash classification, computer vision, deep neural networks.