Abstract The outwardly propagating spherical flame (OPF) method is popularly used to measure the laminar flame speed (LFS). Recently, great efforts have been devoted to improving the accuracy of the LFS measurement from OPF. In the OPF method, several assumptions are made. For examples, the burned gas is assumed to be static and in chemical equilibrium. However, these assumptions may not be satisfied under certain conditions. Here we consider low-pressure and super-adiabatic propagating spherical flames, for which chemical non-equilibrium exists and the burned gas may not be static. The objective is to assess the chemical non-equilibrium effects on the accuracy of LFS measurement from the OPF method. Numerical simulations considering detailed chemistry and transport are conducted. Stoichiometric methane/air flames at sub-atmospheric pressures and methane/oxygen flames at different equivalence ratios are considered. At low pressures, broad heat release zone is observed and the burned gas cannot quickly reach the adiabatic flame temperature, indicating the existence of chemical non-equilibrium of burned gas. Positive flow in the burned gas is identified and it is shown to become stronger at lower initial pressure. Consequently, the LFS measurement from OPF at low pressures is not accurate if the burned gas is assumed to be static and at chemical equilibrium. For super-adiabatic spherical flames, the burned gas speed is found to be negative due to the local temperature overshoot at the flame front. Such negative speed of burned gas can also reduce the accuracy of LFS measurement. It is recommended that the direct method measuring both flame propagation speed and flow speed of unburned gas should be used to determine the LFS at low pressures or for mixtures with super-adiabatic flame temperature.