The operation and management of intelligent transportation systems (ITS), such as traffic monitoring, relies on real-time data aggregation of vehicular traffic information, including vehicular types (e.g., cars, trucks, and buses), in the critical roads and highways. While traditional approaches based on vehicular-embedded GPS sensors or camera networks would either invade drivers' privacy or require high deployment cost, this paper introduces a low-cost method, namely SenseMag, to recognize the vehicular type using a pair of non-invasive magnetic sensors deployed on the straight road section. SenseMag filters out noises and segments received magnetic signals by the exact time points that the vehicle arrives or departs from every sensor node. Further, SenseMag adopts a hierarchical recognition model to first estimate the speed/velocity, then identify the length of vehicle using the predicted speed, sampling cycles, and the distance between the sensor nodes. With the vehicle length identified and the temporal/spectral features extracted from the magnetic signals, SenseMag classify the types of vehicles accordingly. Some semi-automated learning techniques have been adopted for the design of filters, features, and the choice of hyper-parameters. Extensive experiment based on real-word field deployment (on the highways in Shenzhen, China) shows that SenseMag significantly outperforms the existing methods in both classification accuracy and the granularity of vehicle types (i.e., 7 types by SenseMag versus 4 types by the existing work in comparisons). To be specific, our field experiment results validate that SenseMag is with at least $90\%$ vehicle type classification accuracy and less than 5\% vehicle length classification error.