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A high accuracy test of the weak equivalence principle (WEP) is of great scientific signihcance no matter whether its result is positive.We analyze the gravity gradient effect which is a main systematic error source in the test of WEP.The result shows that the uncompensated gravity gradient effect from the coupling term of the dominated gravity gradient multipole moment component q21 and the relative multipole field component Q21 contributes to an uncertainty of 1 × 10-11 on the E(o)tv(o)s parameter.We make a Q21 compensation to reduce the effect by about 20 times,and the limit of the test precision due to this coupling is improved to a level of a part in 1013.