Abstract: For the space-borne timekeeping system, the relativistic effect has an important impact on the clock measurement accuracy. This paper introduces the relativistic theory into the research on wide range time-space transfer due to clock measurement error. The components and magnitudes of various relativistic effects for clocks are derived. Clock frequency adjusting and real-time periodic compensating are confirmed useful to eliminate relativistic effects. For time synchronization and transfer on common Earth-orbiting satellites, aircrafts and moon probes, an interval frequency adjustment, an improved error-restrict interval frequency adjustment and a leap seconds method are proposed to restrict secular relativistic effect errors when the clocks lack of frequency adjustable resolution, it is also proposed to predict periodic errors by building a cross correlation function when unable to get the clocks real-time position and velocity. The simulations show that the analysis and proposed error eliminating methods are effective, and they be used to improve clock synchronization for the future deep space explore.