Rapid and accurate recognition and classification of vehicles are essential for the Intelligent Transportation System (ITS) of Bangladesh. The paper presents a deep learning-based object detection model called Vehicle-YOLOv7 that can detect and classify moving vehicles in real-time on the Padma Multipurpose Bridge (PMB) in Bangladesh. Initially, six hundred-fifty-five (655) still pictures and a video frame containing vehicle images: Bus, Microbus, Car, Truck, Minitruck, Pickup, and Trailer are collected from the PMB to create an original PMB-vehicle image dataset. Thereafter, pre-processing techniques and augmentation processes were employed to produce a training dataset of 7205 image samples. The model was trained and tested using 80% and 20% of the images respectively. Two variations of the YOLOv7 model were evaluated. The Vehicle-YOLOv7 (i.e., YOLOv7x) model performed better than the YOLOv7 model and other state-of-the-art vehicle identification models. The proposed model attained accuracy (A), precision (P), Recall (R), F1-score, and mean-average-precision (mAP) of 98.12%, 97.20%, 98.0%, 96.80%, and 96.86%, respectively. The model accurately detected vehicles with a bounding box and showed detection score and classified the moving vehicles into eight classes: Bus, Microbus, Car, Truck, Minitruck, Motorcycle, Pickup, and Trailer. In addition, the proposed model automatically calculated the vehicles' toll, which reduces the complexity of toll collection by ITS. Therefore, the Vehicle-YOLOv7 detection model is a trustworthy method that can be used to detect and classify the vehicles in the ITS of Bangladesh.