A preconditioning iterative method was applied to the numerical computation of natural convection in a confined region by the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm. The preconditioning was carried out by multiplying the matrix which consists of the entries of the coefficient matrix of a linear system of equations. It was concluded that the preconditioning is especially effective for the linear system of equations whose degree of diagonal dominance of the coefficient matrix is weak, such as of pressure correction. The computational time with the proposed preconditioning iterative method in the present study was almost 2.3 times faster than that by the standard SIMPLE algorithm.