I have a large sparse matrix which is symmetric for the location of non zero values, but the values are different. Could I still use the CG method? I don't have much knowledge of linear algebra, the matrix comes form the discretization of some PDEs and is very large, GMRES method is not appealing because of the need of the calculation with Arnoldi algorithm and storage of the basis.
The BiConjugate Gradient method (BiCG) or its stabilized variant (BiCGSTAB) are Krylov subspace methods that are designed to work on non-symmetric matrices. Given a choice between the two, you should use BiCGSTAB, since it tends to converge more quickly. https://en.wikipedia.org/wiki/Biconjugate_gradient_stabilized_method