The authors study a model of prostate cancer growth and chemotherapy, where the critical nutrient controls the advancement of the tumor. It consists of a system of three (coupled) semilinear parabolic equations: an Allen-Cahn-type equation which describes the tumor phase, a reaction-diffusion equation controlling the nutrient properties and an additional reaction-diffusion equation which governs the concentration of prostate-specific antigen in the prostatic tissue. The first equation is accompanied by the homogeneous Dirichlet boundary condition and the other two equations, by the homogeneous Neumann condition. The solution operator associated with the corresponding initial-boundary value problem defines a strongly continuous semigroup on a suitable phase space. The authors show that this semigroup admits a global attractor and then establish a long time behaviour result for the considered initial-boundary value problem.