In the numerical simulation of heat transfer and fluid flow problems, residual is often adopted as a convergence criterion. Since residual is susceptible to several factors, such as the property of physical problems, the expression form of discretized equations, the scale of grid and the nondimensionalization of governing equations, the converged value differs greatly in different cases. Thus, it is hard to set a specific residual value in a specific numerical calculation. To give a universal convergence criterion in this paper, a residual based on normalization idea is proposed. Range of specified values of this improved convergence criterion for general heat transfer and fluid flow problems is also given in this paper. Numerical simulation results indicate that the improved convergence criterion based on normalized residual is much more reasonable than the one based on traditional residual. (C) 2015 Elsevier Ltd. All rights reserved.