Abstract: Based of the synoptic facts and the simple form of Green's function. for the solution of the elliptic adjoint boundary-value problem, an iterative method suitable for solving the second-order elliptic self-adjoint partial differential equations arising-in meteorology is given. It is quite general. The approximate methods, generally used in meteorology, such as Belousov's, Mashkovitch's, Fjortoft's and the extrapolated Liebmann's technique may be considered as special cases of the present method. Based on the general form of the present method the accuracy and convergence of the above mentioned techniques may be examined and further the ways of improve them may also be given. As a numerical test of, the present method, formula Ih equation(2.7) was used in solving the balanced equation. Table 1 and 2 are the examples of the calculate results.