Performing data mining on large waveform datasets of a high-power laser facility is an important way to achieve precise regulation of a device. However, there are currently issues with missing values, noise, and inconsistency in this database of measuring pulse waveform in a current high-power laser facility. In this paper, a UNet of a series residual module is presented to predict the pulse waveform of a front-end chained system in a current high-power laser facility. The designed network is trained on grouped sequences formed by experimentally measuring pulse waveforms of a high-power laser facility. The strategies of relay output and relay loss are employed in training in order to enable the network to predict two kinds of pulse waveforms simultaneously. The trained network achieved an RMSE of 3.38% on the testing set of measuring pulse waveform at a frequency of 1 Hz, and an RMSE of 0.84% on the testing set of setting the voltage of the Arbitrary Waveform Generator (AWG). These results indicate that this method can accurately fill in paired missing values in the waveform database of a high-power laser facility. The main advantage of this method is that it can quickly couple operational parameters for prediction, and this method can be applied to predicting laser performance, cleaning one-dimensional sequences, and maintaining a waveform database.