Highlights - Combustion instabilities in a pre-mixed lean-burn natural gas engine were studied. - Effect of gas injection timing on the complexity of combustion system was analysed. - Analysis is based on return map, recurrence plot, recurrence quantification analysis. - Source of combustion instabilities is identified based on 3-D CFD simulation. Abstract The cyclic combustion instabilities in a pre-mixed lean-burn natural gas engine have been studied. Using non-linear embedding theory, recurrence plots (RPs) and recurrence qualification analysis (RQA), the hidden rhythms and dynamic complexity of a combustion system in high dimensional phase space for each gas injection timing (GIT) have been examined, and the possible source of combustion instabilities has been identified based on 3-D computational fluid dynamics (CFD) simulation. The results reveal that for lower engine load, with the decrease of mixture concentration, the combustion instability and complexity of combustion system become more sensitive to the variation of GITs. Richer mixture and earlier (GIT 90°CA ATDC) gas injection will lead to more stable combustion, regular oscillatory and low complexity of combustion system, while leaner mixture together with the medium GITs (from 30 to 90°CA ATDC) easily leads to increase of combustion fluctuations, time irreversibility and dynamic complexity of combustion system. When GITs are changed, the combustion instabilities of pre-mixed lean-burn natural gas engines are from in-cylinder unreasonable stratification of mixture concentration and turbulent motion.