This paper concentrates on the problem of designing H<sub>2</sub> state-feedback controllers for continuous-time Markovian jump linear systems (MJLSs) with more general transition rates. The elements in the considered transition rates matrix include completely known, boundary known and completely unknown ones. Some new techniques are proposed to deal with transition probabilities, and less conservative conditions than those in  for H<sub>2</sub> performance analysis of MJLs are obtained in the framework of linear matrix inequalities. Moreover, the unknown transition probabilities can be decoupled from the Lyapunov matrices. As a result, new sufficient conditions for H<sub>2</sub> controller vis state feedback are proposed. Finally, a numerical example is given to verify the effectiveness and superiority of the proposed method.