In the fiber Bragg grating (FBG) sensor network, the signal resolution of the reflected spectrum is correlated with the network's sensing accuracy. The interrogator determines the signal resolution limits, and a coarser resolution results in an enormous uncertainty in sensing measurement. In addition, the multi-peak signals from the FBG sensor network are often overlapped; this increases the complexity of the resolution enhancement task, especially when the signals have a low signal-to-noise ratio (SNR). Here, we show that deep learning with U-Net architecture can enhance the signal resolution for interrogating the FBG sensor network without hardware modifications. The signal resolution is effectively enhanced by 100 times with an average root mean square error (RMSE) < 2.25 pm. The proposed model, therefore, allows the existing low-resolution interrogator in the FBG setup to function as though it contains a much higher-resolution interrogator.