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In this paper we study the following nonlinear BSDE:y(t)+∫1t f(s,y(s),z(s))ds+∫1t[z(s)+g1(s,y(s))+εg2(s,y(s),z(s))]dWs = ξ,t ∈[0,1],where ε is a small parameter.The coefficient f is locally Lipschitz in y and z,the coefficient g1 is locally Lipschitz in y,and the coefficient g2 is uniformly Lipschitz in y and z.Let LN be the locally Lipschitz constant of the coefficients on the ball B(O,N)of Ra × Ra×r.We prove the existence and uniqueness of the solution when LN～ √log N and the parameter εis small.