We study the existence and the global stability of stationary solutions for nonlinear stochastic functional differential equations with additive white noise. Under the condition that the global Lipschitz constant of nonlinear term  is less than the absolute value of the top Lyapunov exponent for the linear flow  with  being monotone or anti-monotone, we show that the infinite-dimensional stochastic flow generated by stochastic functional differential equations with additive white noise possesses a unique globally attracting random equilibrium in the state space of continuous functions, which produces the globally stable stationary solution. Our result is based on the theory of infinite-dimensional random dynamical systems, which can be applied to various stochastic delay differential equations.