We propose the asymmetric multiscale detrended cross-correlation analysis (MS-ADCCA) method and apply MS-ADCCA method to explore the existence of asymmetric cross-correlation for daily price returns in US and Chinese stock markets and to assess the properties of these asymmetric cross-correlations. The results all show the existences of asymmetric cross-correlations, while small asymmetries at small scales and larger asymmetries at larger scales are also displayed. There is a strong similarity between S&P500 and DJI, and we reveal that the asymmetries depend more on the cross-correlations of S&P500 vs. DJI, S&P500 vs. NQCI, DJI vs. NQCI, and ShangZheng vs. ShenCheng when the market is falling than rising, respectively. By comparing the spectra of S&P500 vs. NQCI and DJI vs. NQCI with uptrends and downtrends, we detect some new characteristics which lead to some new conclusions. Likewise, some new conclusions also can be drawn by the new characteristics displayed through the comparison between the spectra of ShangZheng vs. HSI and ShenCheng vs. HSI. Obviously, we conclude that although the overall spectra are similar and one market has the same effect when it is rising and falling in the study of asymmetric cross-correlations between it and different markets, the cross-correlations and asymmetries on the trends of the different markets are all different. MS-ADCCA method can detect the differences on the asymmetric cross-correlations by different trends of markets. Moreover, the uniqueness of cross-correlation between NQCI and HSI can be detected in the study of the asymmetric cross-correlations, which confirms that HSI is unique in the Chinese stock markets and NQCI is unique in the US stock markets further.