Five-axis machining center, combined three linear and two rotary axes, has been increasingly used in complex surface machining. However, as the two additional axes, the machined surface under table coordinate system is usually different from the tool motion under machine coordinate system, and as a result, it is very tough to predict the machined shape errors caused by each axes error motions. This research presents a new kind of sensitivity analysis method, to find the relationship between error motions of each axis and geometric errors of machined shape directly. In this research, the S-shaped machining test is taken as a sample to explain how the sensitivity analysis makes sense. The results show that the presented sensitivity analysis can investigate how the error motions affect the S-shaped machining accuracy and predicted the influence of error motions on certain positions, such as the reversal errors of the axes around motion reversal points. It can be proved that the presented method can help the five-axis machining center users to predict the machining errors on the designed surface of each axes error motions.