Cultural heritage is the asset of all the peoples of the world. The preservation and inheritance of cultural heritage is conducive to the progress of human civilization. In northwestern China, there is a world heritage site -- Mogao Grottoes -- that has a plenty of mural paintings showing the historical cultures of ancient China. To study these historical cultures, one critical procedure is to date the mural paintings, i.e., determining the era when they were created. Until now, most mural paintings at Mogao Grottoes have been dated by directly referring to the mural texts or historical documents. However, some are still left with creation-era undetermined due to the lack of reference materials. Considering that the drawing style of mural paintings was changing along the history and the drawing style can be learned and quantified through painting data, we formulate the problem of mural-painting dating into a problem of drawing-style classification. In fact, drawing styles can be expressed not only in color or curvature, but also in some unknown forms -- the forms that have not been observed. To this end, besides sophisticated color and shape descriptors, a deep convolution neural network is designed to encode the implicit drawing styles. 3860 mural paintings collected from 194 different grottoes with determined creation-era labels are used to train the classification model and build the dating method. In experiments, the proposed dating method is applied to seven mural paintings which were previously dated with controversies, and the exciting new dating results are approved by the Dunhuang expert.