Purpose: This paper aims to propose a new highly efficient iterative method based on classical Oseen iteration for the natural convection equations. Design/methodology/approach: First, the authors solve the problem by the Oseen iterative scheme based on finite element method, then use the error correction strategy to control the error arising. Findings: The new iterative method not only retains the advantage of the Oseen scheme but also saves computational time and iterative step for solving the considered problem. Originality/value: In this work, the authors introduce a new iterative method to solve the natural convection equations. The new algorithm consists of the Oseen scheme and the error correction which can control the errors from the iterative step arising for solving the nonlinear problem. Comparing with the classical iterative method, the new scheme requires less iterations and is also capable of solving the natural convection problem at higher Rayleigh number.