In recent years, considerable literature has proposed the more general class of exponential L´evy processes as the underlying model for prices of financial quantities, which thus better explain many important empirical facts of financial markets. Finite moment log stable (FMLS), CGMY and KoBoL are chosen from those abovementioned models as the dynamics of underlying equity prices in this paper. With such models pricing barrier options, one kind of financial derivatives, is transformed to solve specific fractional partial differential equations (FPDEs). This study focuses on numerically solving these FPDEs via the fully implicit scheme, with the shifted Gr¨unwald approximation. The circulant preconditioned generalized minimal residual method which converges very fast with theoretical proof is incorporated for solving resultant linear systems. Level-2 circulant preconditioner is also proposed to handle the two-dimensional fractional diffusion models. Numerical examples are given to demonstrate the effectiveness of the proposed preconditioner and show the accuracy of our method compared with that done by the Fourier cosine expansion method as a benchmark.