In the framework of self-adaptive turbulence eddy simulation (SATES), a novel SATESsigma turbulence model is developed based on sigma subgrid-scale model in the current work. This model is implemented in the high-fidelity numerical investigation of cold and combusting flow past a v-gutter flameholder. In comparison with available experimental data, the reliability and performance differences between the newly developed SATES-sigma model and the previous SATESSmagorinsky model in cold state and combustion calculation are compared and analyzed. It shows that the SATES-sigma model proposed in this paper accurately predicts the complex turbulent wake. Further, combined finite-rate/eddy dissipation combustion model to simulate the reacting flows, the SATES-sigma model is significantly better than the SATES-Smagorinsky model in the prediction of combustion field, which shows high application potential in turbulent combustion applications.