For the stabilization problem of Markovian jump systems, whose system matrices are unknown, a kind of controller containing state feedback control and adaptive control simultaneously is proposed. Based on the linear inequality matrix technique, the corresponding parameters needed in the designed controller can be solved easily. Compared with some existing adaptive methods, not only the estimated errors are bounded almost surely, but also the states of the resulting closed-loop system are asymptotically stable almost surely. In this sense, the adaptive control method has a better convergence performance in terms of system states asymptotically stable in probability. Furthermore, more extension on the transition rate matrix being partially unknown is considered. A numerical example is given to illustrate the effectiveness of the proposed method.