This note investigates the existence and uniqueness as well as the stability of the general decay rate of the global solution for neutral stochastic differential equations with time-varying delay under a locally Lipschitz condition, a contractive condition, and a monotonicity condition. The stability results are derived by using the Lyapunov function approach and some stochastic analysis techniques, which not only cover the exponential stability in the pth(p > 0)-moment and the almost sure exponential stability, but also the polynomial stability in the pth(p > 0)-moment and the almost sure polynomial stability. Two examples including one coupled system consisting of a mass-spring-damper connected to a pendulum and the nonlinear external random force are given to illustrate the effectiveness of the obtained results.