The confined environment plays a very important role in the phase separation of copolymers, which can change bulk phase behaviors of copolymers. The different confinement conditions can induce the formations of various interesting and novel morphologies, which can be used in a variety of nanotechnology applications such as high-density medium storage, nanolithography and photonic crystals. The grafting of polymers to confined surfaces is an efficient means for tailoring surface properties. In this work, we investigate the effect on architecture of the AB diblock copolymer confined between mixed brush-grafted surfaces by using self-consistent field theory. The brush contains two types of homopolymers. We study the effects of the fraction of A block, grafted period and the volume fraction of the polymer brush, the distance between two surfaces and the interaction strength between two blocks on the morphology. 1) With the increase of the fraction of A block (fA), the phase morphology changes from the A-block hexagonal cylinder to the parallel lamellae, to the curving lamellae, and then to the B-block hexagonal cylinder. The period of hexagonal cylinder and curving lamellae is equal to the grafted period of the polymer brush due to the influence of the polymer brush. 2) The grafted period of polymer brush is a very important factor for the morphology of diblock copolymer. When fA=0.3, we change the grafted period of the polymer brush. We obtain the phase transition from the hexagonal cylinder to the alternating phase of tetragonal and hexagonal cylinder, then to the alternating phase of tetragonal and octagonal cylinder. When fA=0.4, the structure changes from the hexagonal cylinder to the order phase of the waving lamellae and cylinder with the increase of the grafted period of the polymer brush. Compared with the single homopolymer brush system, the mixed brush enlarges the range of ordered phase and reduces the range of disordered phase. Block copolymers are prone to forming cylinder in mixed brush system and tending to form lamellae in single homopolymer brush system. 3) When fA=0.3, we obtain the phase transition from the hexagonal cylinder to the one-layered cylinder phase by increasing the volume fraction of the polymer brush. This transition is different from that of the single homopolymer brush system. Interestingly, when fA=0.45, the structure of AB block copolymer changes from the parallel lamellae to the perpendicular lamellae with the increase of the volume fraction of the polymer brush. The entropic energy plays an important role in this transition process. Similarly, we also observe the phase transition from the parallel lamellae to the perpendicular lamellae by decrease the distance between two surfaces. 4) We construct the phase diagram for a range of the fraction of A block and the interaction strength. The results provide an effective approach to obtaining the desired microstructures for fabricating nanomaterials.