In this paper, two iterative methods are constructed to solve the operator equation Lu = f where L : H → H is a bounded, invertible and self-adjoint linear operator on a separable Hilbert space H. By using the concept of fusion frames, which is a generalization of frame theory, we design some algorithms based on Chebyshev polynomials and adaptive one according to conjugate gradient iterative method, and accordingly, we then investigate their convergence via their correspond convergence rates.