X-ray free-electron lasers (XFELs) have allowed the imaging of nanoscale samples in near-physiological conditions. To achieve three-dimensional (3D) nanostructural reconstruction, many challenges need to be addressed, such as sample delivery for data collection and data processing of noisy diffraction patterns. Here, we provided a demonstration of the 3D structure reconstruction of a gold nanoparticle from XFEL diffraction data measured at the SPring-8 Angstrom Compact Free-Electron Laser using microliquid enclosure arrays (MLEAs) sample holders. MLEAs enable in-solution measurements, however, they induce a significant amount of background noise. Thus, we performed a series of data analyses to identify the diffraction patterns suitable for 3D reconstruction as well as nonhit patterns to estimate the background noise. The background subtraction from the data significantly improved the quality of the restored structure, with the resolution estimated to be 5 nm using Fourier shell correlation. Our paper has revealed the notable potential of XFEL imaging using MLEAs in combination with the developed data-analysis protocol.