X-ray luminescence computed tomography (XLCT) based on x-ray-excitable nanophosphors has been proposed as a new modality for molecular imaging. The technique has two main advantages compared to other modalities. First, autofluorescence, which is problematic for fluorescence imaging, can be substantially reduced. Second, deep-tissue in vivo imaging with high optical contrast and spatial resolution becomes achievable. Here, we extend the novel XLCT modality from the visible or infrared region to a shortwave infrared wavelength by developing an x-ray-induced shortwave infrared luminescence computed tomography (SWIR-XLCT). For this application, rare-earth nanophosphors (RENPs) were synthesized as core/shell structures consisting of a Ho-doped NaYbF4 core surrounded by a NaYF4 shell that emit light efficiently in the shortwave infrared spectral region under x-ray excitation. Through numerical simulations and phantom experiments, we showed the feasibility of SWIR-XLCT and demonstrated its potential for x-ray luminescence imaging with high spatial resolution and deep depth.