The transient properties (mean first passage time T)of the tumor cell growth system driven by color Gaussian 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 T behaves with different characters in the cases of 0λλλλT exhibits complex behavior, namely T has one maximum with the multiplicative noise intensity D and its self-correlation time τ1 increasing.