Vehicle make and model recognition (VMMR) using still images is a challenging research problem. Automatic VMMR systems have many real-life applications that include surveillance. In this paper, initially, we have used five standard convolutional neural network (CNN) models, namely Inceptionv3, Xception, InceptionResNetv2, MobileNetV2, and ResNet152v2 for VMMR. We have also used an attention mechanism to these models. To increase accuracy of the overall model, we have chosen three best base learners from these five CNN models, and formed an ensemble model. The final model is called XMR_Net, where X stands for Xception, M stands for MobileNet, and R stands for ResNet152v2. For experimental evaluation, we have used two benchmark datasets, a recently published dataset called Vehicle Images dataset and VMMRdb-53 dataset. We have achieved satisfactory outcomes with accuracy scores of 95% and 87% (Top-3) on Vehicle Images and VMMRdb-53 datasets, respectively using the proposed XMR_Net model, which is better than its constituent base models. The code and detailed results can be found at: https://github.com/JUVCSE/XMRNET .