This paper investigates the asymptotic stability in distribution of stochastic systems with semi-Markovian switching whose transition rates are time varying, which are more general than stochastic systems with Markovian switching. Some sufficient conditions for the asymptotic stability in distribution of stochastic systems with semi-Markovian switching are established and those conditions are employed to design the state-feedback controllers in terms of linear matrix inequalities. Finally, several examples are given to illustrate the effectiveness of the theoretical results.