The understanding of phase behavior of copolymer brushes is of fundamental importance for the design of smart materials. In this paper, we have performed classical density functional theory calculations to study diblock copolymer brushes (A-B) in an explicit solvent which prefers the A block to B block. With increasing B-block length (NB), we find a structural transition of the copolymer brush from mixed to collapsed, partial-exposed, and exposed structure, which is qualitatively consistent with experiments. The phase transitions are attributed to the interplay between entropic cost of folding copolymer brushes and enthalpic effect of contact between unlike components. In addition, we examine the effect of different parameters, such as grafting density (ρg), the bottom block length (NA), and the chain length of solvent (NS) on the solvent response of copolymer brushes. The transition chain length (NB) increases with decreasing ρg and NA, and a smaller solvent molecule makes the collapsed structure less stable due to its lower penetration cost. Our results provide the insight to phase behavior of copolymer brushes in selective solvents from a molecular view.