The Fast Auxiliary Space Preconditioning (FASP) method is a general framework for constructing effective preconditioners for solving discretized partial differential equations (PDEs). By constructing appropriate auxiliary spaces, FASP transforms a complicated problem into a sequence of simpler solver-friendly systems. In this paper, we present a new FASP preconditioner for petroleum reservoir simulations. According to the analytic characteristics for the pressure and saturation variables in the black oil model, we choose appropriate auxiliary spaces for different parts of the Jacobian systems arising from the fully implicit method (FIM) with coupled implicit wells. By combining the new preconditioner with Krylov subspace methods (such as the GMRes method), we construct an efficient and robust solver, which can be easily generalized to more complicated models like the modified black oil model for simulating polymer flooding. Preliminary numerical experiments demonstrate the advantages of this new preconditioner.