Identifying combustion regimes is important for understanding combustion phenomena and the structure of flames. This study proposes a combustion regime identification (CRI) method based on rotated principal component analysis (PCA), clustering analysis and the back-propagation neural network (BPNN) method. The methodology is tested with large-eddy simulation (LES) data of two turbulent non-premixed flames. The rotated PCA computes the principal components of instantaneous multivariate data obtained in LES, including temperature, and mass fractions of chemical species. The frame front results detected using the clustering analysis do not rely on any threshold, indicating the quantitative characteristic given by the unsupervised machine learning provides a perspective towards objective and reliable CRI. The training and the subsequent application of the BPNN rely on the clustering results. Five combustion regimes, including environmental air region, co-flow region, combustion zone, preheat zone and fuel stream are well detected by the BPNN, with an accuracy of more than 98% using 5 scalars as input data. Results showed the computational cost of the trained supervised machine learning was low, and the accuracy was quite satisfactory. For instance, even using the combined data of CH4-T, the method could achieve an accuracy of more than 95% for the entire flame. The methodology is a practical method to identify combustion regime, and can provide support for further analysis of the flame characteristics, e.g., flame lift-off height, flame thickness, etc.