  We develop a systematic and efficient approach for numerically solving the
non-Markovian quantum state diffusion equations for open quantum systems
coupled to an environment up to arbitrary orders of noises or coupling
strengths. As an important application, we consider a real-time simulation of a
spin-boson model in a strong coupling regime that is difficult to deal with
using conventional methods. We show that the non-Markovian stochastic
Schr\"{o}dinger equation can be efficiently implemented as a real--time
simulation for this model, so as to give an accurate description of spin-boson
dynamics beyond the rotating-wave approximation.
