Linear solvers and parallel computing are crucial for developing a new generation reservoir simulator. To acquire satisfied acceleration performance, we study the parallel algorithms of linear solvers with preconditioners on GPUs (Graphics Processing Units). The classical GMRES solver is implemented, and the parallelization of ILU(0) and ILUT preconditioners based on the Restricted Additive Schwarz (RAS) method is studied. We also develop a parallel triangular solver to solve preconditioner systems on GPUs. The numerical experiments demonstrate our ILU preconditioned solver has favorable acceleration performance against a traditional CPU.