Data synchronization of digital intelligent electronic device（IED） with non-synchronous sampling of electronic transformers is studied. Based on derivative precise error formula of first-order Lagrange interpolation algorithm， each instantaneous error and phasor error of inside and outside interpolation algorithms are calculated， and the impacts to relay protection and measurement are also analyzed. First-order Lagrange interpolation error is related to sampling rate and offset time. But conventional reduce errors method is increasing sampling rate only. Through study on error variation rule with offset factor， and with using parabola equation to fit complex error locus equation by least square method under the certain error， the analysis is simplified. An adaptive adjusting basic time of interpolation algorithm is put forward which can effectively reduce error proved by verification.