The adsorption of polymer on surface is a hot topic in physical, chemical and biological communities, which is influenced by many factors, such as the topological structure and the flexibility of the polymer, the attractive interaction between the polymer and the surface, the detailed structure of the surface, etc. The adsorption of polymers on solid surfaces is extensively studied, while the adsorption behaviors of polymers on soft surfaces are still unclear.In this work, the static and dynamical characters of the adsorption of a free polymer chain on polymer brushes are studied by using Monte Carlo simulation. The brush is formed by grafted polymers with length N_b and distance d. Results indicate that, with increasing the adsorption energy (ε) between the free polymer and the brush, the free polymer shows a phase transition from a desorbed state to an adsorbed state. Based on the dependence of the number of the adsorption segment of the free polymer (m_ad) on the adsorption energy ε, we defined the critical adsorption point (ε_C) where the phase transition occurs. ε_C is nearly independent of the length of the free polymer, but it increases with decreasing the length of the grafted polymer or increasing the distance between the grafted polymers. When ε < ε_C, the free polymer is desorbed and its size is the same as that in free space. When ε ≈ ε_C, the free polymer is sucked into the brush and meanwhile the size is compressed. While when ε$\gg $ε_C, the free polymer is strongly adsorbed on the surface of the brush and forms a quasi two-dimensional conformation, and meanwhile the whole adsorption process contains two stages: the adsorption process of the free polymer and the diffusion process of the brush. Moreover, with the increase of ε, the diffusion of the free polymer shows an obvious transition from the normal model to the sub-diffusion model near ε_C. The transition of the diffusion model maybe useful for separation of polymers with different attractive polymer-brush interactions. For example, one may construct a brush surface and use it as a polymer separation device. Under weak driving force parallel to the surface, polymers with polymer-brush interaction ε < ε_C can move quickly, while polymers with ε > ε_C will move slowly or be trapped on the brush.