A motion analysis based on quaternion processing was performed on an acceleration data acquired with an on-board recorder at usual driving. Three dimensional acceleration time series data was transformed into a quaternion spectral coefficient series. Major motion components were extracted according to the index values estimated from those coefficients. And its phase information could be observed on the display with the ellipses and a color bar code. The characteristics of those components corresponded to the dynamic states of the vehicle's motion. Such analysis is useful as a tool for rapid access to the desired part of huge acceleration database or the long data record.