A two-stage functional boxplot is introduced for the visualization and exploratory data analysis of multivariate curves. Specifically, the original functional boxplot is combined with an outlier-detection procedure on the basis of the functional directional outlyingness, which accounts for both the magnitude and shape outlyingness of functional data. This combination is robust to various types of outliers and, hence, captures the data structures more accurately than does the functional boxplot alone. It also allows for both marginal and joint analysis of the multivariate curves. We apply the proposed tool to Spanish weather data in an illustrative example. © 2018 John Wiley & Sons, Ltd.