The research explores the dynamic relationship between global crude oil price and food price indices on a sample of monthly data spanning from January 1990 to June 2017 within a nonlinear framework. Linear methods are applied first to examine the stationarity, co-integration and linear Granger causality of the variables of crude oil and food price indices. Moreover, a series of nonlinear tests are used to detect the nonlinearity of the univariate and oil-food prices link. Finally, the asymmetric adjustment analyses are made to understand the dynamic vary mechanism depending on the considered regime of the threshold vector autoregressive model (TVAR), and the threshold vector error correction model (TVECM) is integrated to check how the variables respond to the deviations from the equilibrium. The findings of systematic tests and analyses confirm the fact that there is a nonlinear causal relationship between global crude oil and food price indices. The co-movement of crude oil and food price has obvious structural break features, which is relevant to the underlying regime. Furthermore, the results also show that the adjustment process of the food price indices towards equilibrium is highly persistent and grows faster than oil price when a threshold is reached. •A new framework is proposed to analyze the volatility spillover effect.•We prove that the relationship between the two is nonlinear and asymmetric.•In TVAR model, the relationship between the two is reversed in different regimes.•In the TVECM model, only the ECT is significant in the food equation of regime 2.