Abstract: A second-order three-level scheme for solving three-dimensional compressible ideal flow problems is presented, and its stability is proved. By carrying out a large number of practical calculations of two-dimensional and three-dimen- sional flow problems, it is shown that advantages of the scheme are good accuracy, reduced computer time, simplicity of formulas, reduced program-hours, and adaptability to practical application. How to apply the scheme to flowfields with discontinuities is discussed in detail in terms of some specific examples. How to construct the difference-nets for different configurations in different flow conditions is also analyzed. Finally, calculated results for some two-dimensional and three-dimensional complex configurations are given here. The results at fig. 8 are compared with the experiments of Ref. 4. It can be seen from the pressure distributions of Ref. 4 that there are really two subsonic regions in this kind of concave flowfields.