The issues of actuator fault reconstruction, sensor fault reconstruction, and state estimation are considered in this article for Markovian jump systems, using a novel adaptive observer approach. First, by utilizing coordinate transformation technology, the original plant is decoupled into two subplants. The actuator faults and sensor faults are separated in different subplants. Then, two novel observers are proposed, respectively. With the two proposed adaptive observers, state estimation, sensor faults, and actuator faults reconstruction can be achieved. Finally, a numerical example is employed to verify the effectiveness of the theoretical results and to make comparisons with some existing fault reconstruction schemes.