The relational measurement based on Markov-switching GRG copula constructed by this paper is harnessed to analyze the dependence structure between WTI (BRENT) crude oil futures price and 12 kinds of Chinese agricultural commodity futures prices. The empirical results show that there exist two structural states of Markov switching between the futures prices of different agricultural commodities and crude oil futures price. The two states have different duration periods, and the degree of correlation with crude oil futures prices varies under different agricultural commodity futures prices. Among all the 12 kinds of agricultural commodity futures, 11 kinds of agricultural commodity futures prices mainly present positive correlations with crude oil futures prices, although the positive correlation differs between non-extreme and extreme conditions. The remaining agricultural commodity futures price is not related to crude oil futures prices.