This paper deals with the $H_{infty}$ performance analysis problems for a class of Markovian jump systems with partially known transition rates and time-delays which are time varying and depend on system mode. Following the recent study on the class of systems, improved sufficient conditions for $H_{infty}$ performance of the underlying systems are derived in form of LMI by constructing a new Lyapunov-Krasovskii functional. Illustrative numerical examples are provided to demonstrate the effectiveness of the proposed approach.