A multimode optical fiber communication system based on mode/mode group division multiplexing (MDM/MGDM) is one of the current research hotspots. Since there are multiple modes/mode groups multiplexed in the system, how to accurately recognize them is one of the key issues for improving the system performance. This article proposed an intelligent recognition model (IRM) of multimode fiber (MMF) supported fiber modes and mode groups based on the deep learning method through the introduction of a convolutional neural network (CNN). The theoretical simulation and experimental studies on the linear polarization (LP) modes and mode groups have been implemented under the influence of noise. Firstly, 10 LP modes (LP01, LP11a/b, LP21a/b, LP0, LP12a/b, and LP31a/b) and corresponding mode groups have been simulated and experimentally generated based on a customized multimode multi-plane light converter (MPLC) and a conventional OM2 MMF. Then a large amount of mode profiles can be obtained to train and test of the IRM. The experimental results show that the recognition rate of modes/mode groups can reach 100% by using the high-resolution mode images. Subsequently, we resized the high-resolution mode images into low-resolution ones, and the recognition performance of the intelligent recognition model under the receiving condition of a low density photodetector array is studied. Experimental results show that a recognition rate of 98.3% can be also realized when the light field information is received by a 4×4 photodetector array. Therefore, this research shows that the proposed intelligent recognition model can recognize the optical fiber modes/mode groups effectively. It also meant that this method has the potential applications in the MDM-based communication systems and intelligent optical performance monitoring.