I want to solve the large linear system of equations like this: A * x = b (1), where x and b are just vectors and A a square 4320000*4320000, sparse and only 7 diagonal of this matrix fill with numbers (this link shows how A is http://postimg.org/image/flrk6zjax/).

I want to know which Sparse Linear Systems solver in Eigen is fast and efficient for this system?

You need to use a SparseMatrix<double> and then, since A is not symmetric, you might try the three different solver and see which one is best for your actual numerical values:

- ConjugateGradient<SparseMatrix<double>, Upper|Lower>
- SparseLU<SparseMatrix<double> >
- BiCGSTAB<SparseMatrix<double> >