In this paper, we study a kind of boundary value problems with integro boundary condition for second order RFDEx"(t) = f(t, xt(.),x(t),x′(t)), t ∈ [0, T],x(t) = ψ(t),t ∈ [-r, 0], ∫0T (a(s)xm(s) + b(s)x′n(s))ds = A.Some new results on the existence and uniqueness are obtained.