The research of the compressible miscible two-phase (oil and water) displacement problem with moving boundary value is of great value to the history of oil-gas transport and accumulation in basin evolution, as well as to the rational evaluation in prospecting and exploiting oil-gas resoures. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary value. For a generic case of two-dimensional bounded region with two classes of boundary value problems, we put forward a kind of characteristic finite difference schemes and make use of thick and thin grids to form a complete set, the calculus of variations, the change of variables and of the theory of prior estimates and teechniques. Optimal order estimates in l~2 norm are derived for the errors in approximate solutions. The research is important both theoretically and practically for model analysis in the field, for model numerical method and for software development.