A local convergence condition of Newton-Laphson's method in solving diseretization nonlinear equation8 of coupled problems is shown and proved.It gives out relation among time-step and space.step and quasi.compres8ion factor. And it provides theoretically an assurance for convergence of Newton.Laphson's method within numerical analysis. Numerical example shows that the time-step in actual calculating can be greater than theoretical value 5lightly.