With a numerical code for solving the boundary-layer equations, the performance of different turbulence models for the natural convection boundary layer for air along a heated vertical plate is tested. The algebraic Cebeci-Smith model, the standard k-ε model with wall functions for k and ε and different low-Reynolds number k-ε models are tested. The Cebeci-Smith model calculates a too low wall-heat transfer and turbulent viscosity. The standard k-ε model with wall functions gives a too high wall-heat transfer, but the velocity and temperature profiles agree reasonably with experiments. Accurate wall-heat transfer results require the use of low-Reynolds number k-ε models; the models of Lam and Bremhorst, Chien, and Jones and Launder perform best up to a Grashof number of 10 11. For larger Grashof numbers the Jones and Launder model is best. A sensitivity study shows that the wall-heat transfer with the standard k-ε model largely depends on the choice of the wall functions for k and ε. Replacing these wall functions by zero wall conditions for k and ε and adding the functions D and ƒ μ of the Chien model to the standard k-ε model gives a simple, but accurate low-Reynolds number k-ε model for the natural convection boundary layer.