This paper is intended for exploring the multifractal features of tanker freight rate market volatility with the common external factor of crude oil price by both the multifractal cross-correlation analysis method (MF-CCA) and the multifractal detrended partial cross-correlation analysis method (MF-DPXA) with consideration of finite size effect. The multifractal spectrums of original, random and surrogate time series are employed to separate the three components of multifractality, and to uncover the influence of financial crisis and oil price on volatility and cross-correlated fluctuations of the tanker freight rates. After the financial crisis in terms of the generalized Hurst exponent, stronger non-linear characteristic and noticeable anti-persistent characteristic in cross correlations between freight rates are supported by the MF-DPXA analysis. Meanwhile, stronger multifractality is indicated by the MF-CCA analysis. These results deepen the understanding of multifractality in tanker freight rate market, and provide investors, shipping related operators or even market players with insight to adjust their marketing strategies. •Deep exploration on multifractality of cross-correlation between tanker freight rates volatility with external factor of crude oil price volatility by means of both MF-DPXA and MF-CCA is studied.•The influence of financial crisis on volatility and cross-correlated fluctuation is uncovered.•Stronger non-linear characteristic after the financial crisis is observed.