A pressure based implicit procedure to solve the Euler and Navier-Stokes equation is developed to predict transonic viscous and inviscid flows around the pitching and heaving airfoils with a high reslution scheme. In this process, nonorthogonal and non moving mesh with collocated finite volume formulation are used. In order to simulate pitching or heaving airfoil, oscillation of flow boundary condition is applied. The boundedness criteria for this procedure are determined from Normalized Variable Diagram (NVD) scheme. The procedure incorporates the K-E eddy- viscosity turbulence model. This process is tested for inviscid and turbulent transoinc aerodynamic flows around oscillation airfoil. The results are compared with other existing numerical solutions and with the experimental data. The comparisons show that the resolution quality of the developed algorithm is significant.