Serial acquisition of one-dimensional NMR spectra appears in many contexts, e.g. in variable-temperature studies or reaction monitoring. In a conventional approach, the spectra are processed separately, and standard peak-picking is performed in each of them. Yet, when chemical shifts change linearly between spectra, the Radon transform (RT) is more effective than conventional data processing, since it provides sensitivity and resolution gains. RT results in a two-dimensional (2D) spectrum with one dimension corresponding to resonance frequencies and the other to their rates of change. However, the lineshapes in 2D RT spectra are not 2D lorentzians, and thus available spectral peak-pickers cannot effectively deal with them. We propose a solution to this problem — a peak-picker dedicated to 2D RT spectra and based on a U-Net neural network. The software contains a user-friendly graphical interface. We test the program on three challenging serial data sets to demonstrate the robustness to peak overlap, complex multiplet structures and low signal-to-noise ratio.