The paper is concerned with finite-time dissipativity analysis and design for stochastic Markovian jump systems with generally uncertain transition rates and time-varying delay. By constructing a more appropriate Lyapunov–Krasovskii functional, sufficient conditions for finite-time dissipativity of the underlying system are first proposed. Then, a state feedback controller is designed such that the closed-loop Markovian jump system is finite-time dissipative. These sufficient criteria are derived in the form of linear matrix inequalities (LMIs). Finally, numerical examples are given to demonstrate the validity of the main results.