Due to the small core diameter, a single-core multimode fiber (MMF) has been extensively investigated for endoscopic imaging. However, an extra light path is always utilized for illumination in MMF imaging system, which takes more space and is inapplicable in practical endoscopy imaging. In order to make the imaging system more practical and compact, we proposed a dual-function MMF imaging system, which can simultaneously transmit the illumination light and the images through the same imaging fiber. Meanwhile, a new deep learning-based encoder-decoder network with full-connected (FC) layers was designed for image reconstruction. We conducted an experiment of transmitting images via a 1.6 m long MMF to verify the effectiveness of the dual-function MMF imaging system. The experimental results show that the proposed network achieves the best reconstruction performance compared with the other four networks on different datasets. Besides, it is worth mentioning that the cropped speckle patterns can still be used to reconstruct the original images, which helps to reduce the computing complexity significantly. We also demonstrated the ability of cross-domain generalization of the proposed network. The proposed system shows the potential for more compact endoscopic imaging without external illumination.