The simulation methods based on stochastic realizations of state vector evolutions derived from the time convolutionless master equation are investigated. The quantum jumps for non-Markovian systems and their waiting time distribution is mainly focused on. With the help of an exact analytical waiting time distribution, the non-Markovian quantum trajectory for a stochastic process of a driven two-level system is generated. The effectiveness and superiority of the algorithm is verified by the performance comparing to our previous work in the sense of Markovian prosperities.