The transient properties (e.g., the mean first passage time T) of the gene transcriptional regulatory system driven by colored cross-correlated noise are investigated. The approximate Fokker-Planck equation is obtained based on the Novikov theorem and the Fox approach and the explicit expression of the mean first passage time is derived. The numerical computation results show that for the case of strong correlation intensity and short correlation time，a successive switch process (i.e.，“on”→“off”→“on”) occurs; for tha case of weak correlation intensity and long correlation time，only one switch process occurs (i.e.，“on”→“off”). The reentrance phenomena appear in the gene transcriptional regulatory system.