In the present study, unsteady flow simulations of a variable geometry nozzle were conducted using a two-dimensional flow solver based on hybrid unstructured meshes. The variable geometry nozzle is used to achieve efficient performances of aircraft engines at various operating conditions. To describe the motion of the variable geometry nozzle, an algebraic method based on the basis decomposition of normal edge vector was used for the deformation of viscous elements. A ball-vertex spring analogy was used for inviscid elements. The aerodynamic data were obtained for a range of nozzle pressure ratios, and the validations were made by comparing the present results with available experimental data. The unsteady nozzle flows were simulated with an oscillating diverging section and a converging-diverging section. It was found that the nozzle performances are influenced by the nozzle exit flow characteristics, mass flow rate, as well as unsteady effects. These unsteady effects are shown to behave differently depending on the frequency of the nozzle motion.