In the context of the frequent occurrence of extreme events, measuring the tail dependence of financial time series is essential for maintaining the sustainable development of financial markets. In this paper, a multiscale quantile correlation coefficient (MQCC) is proposed to measure the tail dependence of financial time series. The new MQCC method consists of two parts: the multiscale analysis and the correlation analysis. In the multiscale analysis, the coarse graining approach is used to study the financial time series on multiple temporal scales. In the correlation analysis, the quantile correlation coefficient is applied to quantify the correlation strength of different data quantiles, especially regarding the difference and the symmetry of tails. One reason to adopt this method is that the conditional distribution of the explanatory variables can be characterized by the quantile regression, rather than simply by the conditional expectation analysis in the traditional regression. By applying the MQCC method in the financial markets of different regions, many interesting results can be obtained. It is worth noting that there are significant differences in tail dependence between different types of financial markets.