Abstract: This paper applied the finite volume time-marching method to solving fully three-dimensional transonic flow in turbomachinery.First, characteristic properties of the governing equations in the rotational coordinate system are analyzed. Boundary conditions are also discussed. Then, the computational scheme is formulated from governing equations in the integral form. Essentially, this scheme is an extention of our computational scheme （see [3, 4]） for flow over a plane cascade and cascades to general surface of revolution to fully three-dimensional flow.The advantages of this method are listed as follows;1.It is easily applied to problems with complex geometry.2.Reasonable accuracy can be attained even with a coarse grid.The method has been programmed and some numerical tests have been made.The numerical tests show that the results of fully three-dimensional flow are very close to the corresponding results of plane cascade when the height of the blade is small. They almost coincide with experimental data. Therefore this method appears correct.The numerical tests also demonstrate that the effect of rotation is small, especially it has almost No influence on the Mach number distribution on the pressure surface.Comparison between quasi-three-dimensional and fully three-dimensional solutions in turbomachinery indicates that the quasi-three-dimensional assumptions are possible to lead to significant errors. This confirms the necessity of fully three-dimensional calculation.