An adaptive triangular mesh and a locally implicit finite volume scheme are utilized to investigate the transonic oscillating cascade flows. In the Cartesian coordinate system, the unsteady Euler equations with moving domain effects are solved. Based on the time history of lift coefficient and the magnitude distribution of the first harmonic dynamic pressure difference coefficient, the present approach can efficiently achieve the periodical characteristics and give satisfactory results. From the instantaneous vorticity contours, the vortex-shedding phenomenon due to oscillating unsteadiness is observed. The instantaneous adaptive meshes clearly capture the unsteady pressure wave, shock and vortex-shedding behaviors.