This paper presents a stabilisation problem for singular Markovian jump system with time-varying transition rate based on a reduced-order observer. To design the reduced-order observer, a canonical equivalent form for singular Markovian jump system is given. By the output variables of the equivalent form of singular Markovian jump system and the state of the reduced-order observer, an integral sliding surface is designed. Then, the sufficient condition for the stochastic admissibility of sliding motion is given, in which the time-varying transition rate is handled by the quantized method. Furthermore, a sliding mode controller is developed such that the system can be driven to the sliding surface in finite time. Finally, the effectiveness and superiority of the obtained results are illustrated by two examples, a numerical example and a practical example of DC motor model respectively.