In this talk, a relaxation weighted greedy block Kaczmarz (RWGBK) method is considered for solving the consistent system of bounded linear operators in Hilbert spaces. The method is deterministic and does not require computing the pseudoinverses of linear operators. It is proved under mild conditions that, for any initial point, the method will converge to a solution of the linear system nearest to the initial point, and that the iterative sequence starting from the zero point may converge linearly to the least norm solution. Numerical experiments on an  application of the circular Radon transform are given to illustrate that the considered method  is efficient and that it is necessary to consider the relaxation parameter and weight.