A dynamic state estimation method of integrated natural gas and electric power systems (IGESs) in proposed. Firstly, the coupling model of gas pipeline networks and power systems by gas turbine units (GTUs) is established. Secondly, the Kalman filter based linear DSE model for the IGES is built. The gas density and mass flow rate, as well as the real and imaginary parts of bus voltages are taken as states, which are predicted by the linearized fluid dynamic equations of gases and exponential smoothing techniques. Boundary conditions of pipeline networks are used as supplementary constraints in the system model. At last, the proposed method is applied to an IGES including a 30-node pipeline network and IEEE 39-bus system coupled by two GTUs. Two indexes are used to evaluate the DSE performance under three measurement error conditions, and the results show that the DSE can obtain the accurate dynamic states in different conditions.