Abstract In order to predict error motion of continuous porous journal air bearing, an accuracy model is established to reveal the relationship among error motion, roundness error and structure parameter under quasi-static conditions. Based on the model, averaging coefficient is defined to quantitatively characterize the error averaging ability. The study finds that whether the bush and shaft roundness errors match is the cause of error motion. The trilobal roundness error of shaft has a major impact on accuracy for a porous journal air bearing with an elliptical bush, while the elliptical roundness error of shaft has a major impact on accuracy for that with a trilobal bush. On the two-dimensional plane of bush wave numbers n2 = 2~7 and shaft wave numbers n1 = 2~15, the averaging coefficients are symmetrical along the line n1 = n2. The shaft wave numbers which equal integer multiples of prime numbers of bush wave number have no impact on accuracy, while the remaining shaft wave numbers have impact. Among them, those at points n1 = n2*i ± 1 are with obvious averaging coefficients and have a major impact on accuracy where i is a positive integer. The main peaks of averaging coefficients appear at the points n1 = n2 ± 1, which have the most important impact on accuracy. The theory has many potential applications such as prediction of error motion, structural optimization and selection of parts grinding method, which is of significant importance for design and testing of porous journal air bearings used widely in ultra-precision machine tools.