Abstract: To seek with less conditions to determine the relationship of functions, the uniqueness problem of the meromorphic functions in the angle domain sharing three values was discussed. It established the relationship of the characteristic function S(r, f) and the counting function C(r, f) , sequentially extended the uniqueness of meromorphic functions sharing three values in the whole complex plane by H. Ueda's and the four-value theorem in an angular domain by Zhang Qing-cai, got the three-value theorem in an angular domain.