In this paper, we simulate diffusion bridges by using an approximation of the Wiener-chaos expansion (WCE), or a Fourier-Hermite expansion, for a related diffusion process. Indeed, we consider the solution of stochastic differential equations, and we apply the WCE to a particular representation of the diffusion bridge. Thus, we obtain a method to simulate the proposal diffusion bridges that is fast and that in every attempt constructs a diffusion bridge, which means there are no rejection rates. The method presented in this work could be very useful in statistical inference. We validate the method with a simple Ornstein-Uhlenbeck process. We apply our method to three examples of SDEs and show the numerical results.