Few-mode fiber (FMF), a mode multiplex technique, has been a candidate to provide high transmission capability in next-generation elastic optical networks (EONs), where the probabilistic shaping (PS) technology is widely used to approach Shannon limit. In this paper, we investigate a fast and accurate method of modulation format recognition (MFR) of received signals based on a transfer learning network (TLN) in PS-based FMF-EONs. TLN can apply the feature extraction ability of convolutional neural networks to the analysis of the constellations. We conduct experiments to demonstrate the effectiveness of the proposed scheme in FMF transmissions. Six modulation formats, including 16QAM, PS-16QAM, 32QAM, PS-32QAM, 64QAM and PS-64QAM, and four propagating modes, including LP01, LP11a, LP11b and LP21, are involved. In addition, comparisons of TLN with different structures of convolutional neural networks backbones are presented. In the experiment, the iterations of the TLN are one-tenth that of conventional deep learning network (DLN), and the TLN overcomes the problem of overfitting and requires less data than that of DLN. The experimental results show that the TLN is an efficient and feasible method for MFR in the PS-based FMF communication system.