 This study assesses OpenStreetMap, OSM, building completeness for 12,975 cities worldwide using population grid data as a proxy for reference building data and finds that for 75% of cities, the completeness is lower than 20%, with no more than 9% having an estimated completeness higher than 80%. The overall accuracies of most countries were higher than 80%, and the estimated completeness was highly correlated with the reference completeness. A global and open data set related to OSM building completeness has been made available for public use. This article was authored by Qi Jiu, Yuan Zhong, Kuchang, and others.