Seafloor mapping to create bathymetric charts of the oceans is important for various applications. However, making high-resolution bathymetric charts requires measuring underwater depths at many points in sea areas, and thus, is time-consuming and costly. In this work, treating gridded bathymetric data as digital images, we employ the image-processing technique known as superresolution to enhance the resolution of bathymetric charts by estimating high-resolution images from low-resolution ones. Specifically, we use the recently-developed deep-learning methodology to automatically learn the geometric features of ocean floors and recover their details. Through an experiment using bathymetric data around Japan, we confirmed that the proposed method outperforms naive interpolation both qualitatively and quantitatively, observing an eight-dB average improvement in peak signal-to-noise ratio. Deep-learning-based bathymetric image superresolution can significantly reduce the number of sea areas or points that must be measured, thereby accelerating the detailed mapping of the seafloor and the creation of high-resolution bathymetric charts around the globe.