The finite time reliable control problem for the switched LPV systems with Markovian jump parameters and actuator failures is investigated. The subsystems of the switched systems are described by LPV dynamics, which can describe more general a class systems. A key point of this work relaxes the special requirement of completely known transition rates to more general form that transition rates are incomplete, which may lead to less conservativeness. Firstly, for the switched LPV systems with Markovian jump parameters, the sufficient condition, ensuring the finite time stability, is developed. Secondly, the finite time reliable control problem for the switched LPV systems with Markovian jump parameters and actuator failures is presented, and a finite time reliable controller is designed. Finally, a numerical example is given to demonstrate the applicability of the main results.