About 15,000 angiosperms are dioecious, but the mechanisms of sex determination in plants remain poorly understood. In particular, how Y chromosomes evolve and degenerate, and whether dosage compensation evolves as a response, are matters of debate. Here, we focus on Coccinia grandis, a dioecious cucurbit with the highest level of X/Y heteromorphy recorded so far. We identified sex-linked genes using RNA sequences from a cross and a model-based method termed SEX-DETector. Parents and F1 individuals were genotyped, and the transmission patterns of SNPs were then analyzed. In the >1300 sex-linked genes studied, maximum X-Y divergence was 0.13–0.17, and substantial Y degeneration is implied by an average Y/X expression ratio of 0.63 and an inferred gene loss on the Y of ~40%. We also found reduced Y gene expression being compensated by elevated expression of corresponding genes on the X and an excess of sex-biased genes on the sex chromosomes. Molecular evolution of sex-linked genes in C. grandis is thus comparable to that in Silene latifolia, another dioecious plant with a strongly heteromorphic XY system, and cucurbits are the fourth plant family in which dosage compensation is described, suggesting it might be common in plants.