This paper considers the stability robustness of Markovian jump linear systems in continuous-time with respect to their transition rates. The system under study is a linear continuous-time one with Markovian jump parameters where the mode transition rate is perturbed. By using stochastic Lyapunov function approach and Kronecker product transformation techniques, we developed a sufficient condition for the robust stochastic stability of the underlying system, which is in terms of an upper bound of the perturbed transition rate. A numerical example is presented to show the potential of the proposed technique.