This study proposed a spatial wave measurement method based on a U-net convolutional neural network. First, frame images are extracted from a video collected by a physical model experiment, and a dataset of spatial wave measurements is created and extended using a data enhancement method. A U-net convolutional neural network is built to extract the spatial wave information of the images; evidently, the segmented water level is close to that of the original image. Next, the U-net convolutional neural network is compared with the sensor, pixel recognition, and Canny edge detection methods. Pixel recognition results reveal that the maximum and minimum errors of the U-net convolutional neural network are 3.92% and 1.05%, those of the Canny edge detection are 5.97% and 1.33%, and those of the sensor are 11.8% and 1.6%, respectively. Finally, the nonlinear characteristic quantities of waves are measured using the proposed U-net convolutional neural network. The kurtosis and asymmetry calculated in the spatial domain are slightly larger than those calculated in the time domain, whereas the skewness calculated in the spatial domain is smaller than that calculated in the time domain. The asymmetry and kurtosis increase with an increase in wave height and period, whereas the skewness increases with an increase in wave height but decreases with an increase in period.