This paper investigated a stochastic gene transcriptional regulatory system, in which the noise was considered to be a kind of non Gaussian noise with a long tail. The role of the parameters of this non Gaussian noise in the switching was considered with the stationary probability density. It has been found that noise intensity can not induce a switch, however, stability index and skewness parameter can be taken as the control parameters of gene switch. Additionally, the effects of the parameters on the transition property of the system, defined as the mean first passage time, were also studied.