•In this paper, we examine whether gold or Bitcoin is a safe haven against economic policy uncertainty (EPU).•We combine the GARCH model and quantile regression with dummy variables, which include the extreme situations of average condition and different quantiles.•Hedge and safe-haven roles of gold and Bitcoin against EPU shocks are correlated with their bearish or bullish market situation.•Bitcoin reacts more responsive to EPU shocks and gold maintains stability with smaller hedge and safe-haven coefficients. Calculating the hedge and safe-haven properties of gold and Bitcoin via GARCH model and quantile regression with dummy variables. We find that: (1) Neither gold nor Bitcoin can serve as a strong hedge or safe-haven for economic policy uncertainty (EPU) at the average condition. (2) Bitcoin is more responsive to EPU shocks, while gold maintains stability with smaller hedge and safe-haven coefficients. (3) In most cases, both gold and Bitcoin can act as the weak hedge and weak safe-haven against EPU during the extreme bearish and bullish markets, which two can be considered for portfolio diversification during the normal market.