The observability of time-varying continuous and discrete-time stochastic Markov jump systems(SMJSs) is investigated. Time-varying SMJSs are transformed into the equivalent time-varying linear systems based on the H-representation method. Gramian matrix criteria for the observability of time-varying continuous and discrete-time SMJSs are derived based on the linear system theory. A numerical example is given to demonstrate the correctness of the obtained results.