Abstract Cryptocurrency has experienced the skyrocketing and falling back in 2018. Beyond the hype, the specific price movements of different cryptocurrencies should be investigated in a more careful way. Since the cryptocurrency market is a non-linear complex system which are not suitable analyzed by tradition methods, this paper introduces methods from econophysics. Mono-fractal analysis (detrended fluctuation analysis, DFA) is applied to investigate the price movement. Further, multi-fractal fluctuation detrended analysis (MF-DFA) is used for robustness test. Through analyzing four representative cryptocurrencies, our paper finds a strong momentum effect in BTC and ETH market, and a reversion effect in XRP and EOS when large fluctuation occurs. These findings may provide a reference for trading strategy in alternative asset allocations.