A fast and stable solution of matrix equations formed by a finite volume method as a discretization scheme was investigated in steady flow calculation, especially with non-computational cells and cyclic conditions often used in cylindrical coordinate systems. To simulate a computational domain having complex geometry, a method was developed to form a coefficient matrix discretized by a finite volume method. The matrix equations were iteratively solved by the Bi-Conjugate Gradient Stabilized method with polynomial preconditioning (Bi-CGSTAB), and the calculated results were compared with those given by the Tri-Diagonal Matrix Algorithm (TDMA). Convergence and stability of the iterative calculation and under-relaxation factors are also discussed. No differences between TDMA and Bi-CGSTAB for a solution of matrix equations were found in the calculated results. With a greater number of computational cells, faster convergence was obtained by Bi-CGSTAB than by TDMA. Furthermore, larger under-relaxation factors could be employed for the calculation of Bi-CGSTAB than that of TDMA. Bi-CGSTAB is superior to TDMA giving in fast and stable convergence as a solution of the matrix equations discretized by a finite volume method. Therefore, stable calculation and fast convergence can be obtained using the present method.