Crude oil market pricing power is of great significance to the construction of a high-standard market system and the improvement of factor market operating mechanism. To judge the impact of Shanghai crude oil futures on the pricing power of the crude oil market, a time-varying information share model is constructed based on a multi-scale analysis method to empirically test the dynamic evolution of China’s crude oil market pricing power. The spot price of Daqing crude oil, prices of Brent crude oil futures, WTI crude oil futures, and Shanghai crude oil futures from December 2001 to November 2020 are adopted as the research sample. The research results show that: (1) the price of crude oil futures dominates crude oil market, and the pricing power of each market is relatively stable during the sample period, but it can be affected by extreme events; (2) Shanghai crude oil futures gain a 28.84% pricing share and has shown certain pricing power after its launch, however, its pricing power has much room for improvement on the whole and on high-frequency and medium-frequency time scales. (3) under different time scales, the evolution of crude oil market pricing power shows the characteristics of heterogeneity. On the high-frequency scale, Shanghai crude oil futures receive 31.54% of the pricing power after its introduction. Despite of this pricing power, it does not fill the gap which is caused by the decrease of the pricing power of Daqing spot market. On the medium-frequency scale, the pricing share of Shanghai crude oil futures is lower than pricing power of other frequency domains. On the low-frequency scale, after the introduction of Shanghai crude oil futures, with a pricing share of approximately 45.58%, INE has gained a dominant role. To improve the pricing power of Shanghai crude oil futures, the improvement of the market operation mechanism should be focused on the improvement of pricing power on the high frequency and medium frequency time scales.