Scheme and laboratory demonstration test of composite axes inertial line of sight stabilization of acquisition, tracking and pointing system on moving base are introduced. Inertial angular rate measured by dynamically tuned gyroscope is used to realize bed coarse stabilization in big range and inertial angular position measured by linear accelerometers is used to realize line of sight reference fine stabilization in small range. The coarse stabilization error is composed with line of sight reference stabilization error and the relative error between line of sight reference and its base. Test results show that an arcsecond stabilization accuracy can be acquired with composite axes stabilization scheme.