By applying our previously developed two-step scheme for galaxy morphology classification, we present a catalog of galaxy morphology for H-band-selected massive galaxies in the COSMOS-DASH field, which includes 17292 galaxies with stellar mass M_*_>10^10^M_{sun}_ at 0.5<z<2.5. The classification scheme is designed to provide a complete morphology classification for galaxies via a combination of two machine-learning steps. We first use an unsupervised machine-learning method (i.e., bagging-based multiclustering) to cluster galaxies into five categories: spherical (SPH), early-type disk, late-type disk, irregular (IRR), and unclassified. About 48% of the galaxies (8258/17292) are successfully clustered during this step. For the remaining sample, we adopt a supervised machine-learning method (i.e., GoogLeNet) to classify them, during which galaxies that are well classified in the previous step are taken as our training set. Consequently, we obtain a morphology classification result for the full sample. The t-SNE test shows that galaxies in our sample can be well aggregated. We also measure the parametric and nonparametric morphologies of these galaxies. We find that the Sersic index increases from IRR to SPH and the effective radius decreases from IRR to SPH, consistent with the corresponding definitions. Galaxies from different categories are separately distributed in the G-M_20_ space. Such consistencies with other characteristic descriptions of galaxy morphology demonstrate the reliability of our classification result, ensuring that it can be used as a basic catalog for further galaxy studies.