A high field Nb3Al common coil magnet is under development as an R&D of "Advanced Superconducting Magnets for the LHC Luminosity Upgrade", in the framework of the CERN-KEK cooperation program. The goal of this research is to demonstrate the feasibility of high field magnet wound with Nb3Al cable. The common coil approach and the shell-based structure were adopted in the design of this magnet. Besides three Nb3Al coils, two Nb3Sn coils were included to increase the peak field of the whole magnet. The two types of coils were designed with different straight lengths to reduce the peak field of the Nb3Sn coils. The peak fields of the Nb3Al and Nb3Sn coils are 13.1 T and 11.8 T respectively. An aluminum shell together with four aluminum rods applies stress to the coils to overcome the Lorenz force during excitation. Two different support structures for the superconducting coils were introduced in this paper. The development status is also presented.