Single-layer steel reticulated shell structures have a long history and are widely distributed. As their service life increases, corrosion in these structures becomes an increasingly prominent problem. However, currently, there is nearly no research available on the static behavior of corroded steel reticulated shell structures. Therefore, taking the single-layer steel reticulated shell structure as the research object, an accelerated corrosion test was first carried out on Q345, a commonly used steel for this structure, and an equivalent conversion calculation method was proposed. Then, a Python program (version 3.5.0) for single-layer reticulated shells considering component dimensions, joint stiffness, and random corrosion was written, and numerical simulation analysis was carried out on the static behavior of single-layer steel reticulated shell structures after corrosion. Finally, based on parametric analysis, the random corrosion influence coefficient and joint stiffness influence coefficient were derived, and a calculation method for the elastic–plastic ultimate bearing capacity of the structure was established, which could enhance the current design methods for steel reticulated shells by taking corrosion effects into account. The research results will provide specific and programmed references for the damage identification and safety assessment of single-layer steel reticulated shell structures during their service life in strongly corrosive environments along the coast and offshore, holding important engineering significance and scientific value.