We study a diblock AB copolymer brush in good solvent using the self-consistent field approximation. The copolymer chains of the brush are end grafted to a planar surface always by the same type of monomers. Depending on the Flory-Huggins interaction parameter chi(AB), we found two different regimes. If chi(AB)>0 a demixing transition occurs when the solvent is poor. An exclusion zone appears close to the grafting surface from where one type of monomers is expelled. In this region a steplike brush is formed by the other monomers. At the extremity of this brush appears then a conventional parabolic brush formed by the excluded monomers. If chi(AB)<0 the monomers are miscible and backwards twisted configurations become very important as chi(AB) increases. For larger values of chi AB the collapse of the system may occur.