Submerged offset jets are common in drainage systems, slot fishways, and hydraulics engineering. Surge usually occurs at the free surface downstream of the jet, which may affect the downstream shipping in serious cases. However, the properties of this wave are very different from those of stormy waves. The research results of wave characteristics in the ocean cannot be directly applied to the analysis of hydraulics engineering downstream channels. To analyze the water wave propagation characteristic generated by submerged jets from rectangular orifices, a series of experiments are conducted in this paper. The time-history information of free-surface wave along the propagation path under various upstream water depths was measured, and the Hampel filter combined with wavelet threshold filter was used for data processing. The propagation characteristics of submerged jet water waves in the time domain and frequency domain were obtained. The results indicate that: (i) the data processing method adopted in this paper can reduce the error in data analysis; (ii) the wave height of each measuring point approximately conforms to Weibull distribution. With the rise of upstream water depth, the wave height of each measuring point increases gradually, and the wave height decreases exponentially along the propagation path; (iii) the spectrum analysis shows that the peak and width of the spectrum vary along the propagation path. The relevant research results obtained in this paper further reveal the propagation characteristics of water waves generated by submerged jets and enrich the research content of the jet theory.