Abstract: Abstract A third order accuracy implicit approximate factorized TVD code is developed using Chakravarthy-Osher scheme to solve the steady flows in annular turbine cascades.The governing equation is the 3D Euler equations in arbitary curvilinear coordinate systems in terms of cylinder coordinate system velocity components.Beam-Warming factorization and upwind difference are adopted to discretize the implicit term,and the explicit one is discretized by Chakravarthy-Osher TVD numerical fluxes.The boundary condition is obtained from extrapolation.The resulted algebraic equations are tridiagonal block matric system and solved by sweeping in each direction.So the scheme is a 5 point implicit AF scheme of first order temporal and third order or second order spacial accuracy depending on the two TVD factors.Two examples are presented,the first verifies the calculation of third order scheme with a low speed wind tunnel experiment,the second compares the third order scheme with the second order one.The examples indicate that the code results in numerical solutions agree with the experiment,and the third order scheme has little difference from the second order one in the solutions,but it decreases the convergent residual greatly.Also it is showed that the two schemes do not agree with each other very well in the throat of the cascade where the flow velocity is equal to the local sound speed.