A sensing system for a vehicle includes at least one radar sensor disposed at the vehicle and having a field of sensing exterior of the vehicle. The radar sensor includes an antenna array having multiple transmitting antennas and multiple receiving antennas. Sensed radar data provides a data set of received sensed radar data that is representative of an object in the field of sensing of the at least one radar sensor, and the data set of received sensed radar data is compared to stored data sets representative of a plurality of vehicle types. Responsive to the data set of received sensed radar data being determined to correspond to a particular stored data set, the sensing system classifies the detected object as a particular vehicle type.