The Kaczmarz algorithm is an iterative scheme utilizing alternating projection methods, one of the classically iterative methods applied to solve large systems of hyperdeterministic linear equations. Based on a new and effective probabilistic criterion, for solving large systems of hyperdeterministic linear equations, Bai and Wu1 have proposed the Greedy Randomized Kaczmarz (GRK) algorithm. In this paper, we combine the greedy strategy with the idea of blocking, innovate on the basis of the randomized extended average block Kaczmarz algorithm7, improve the algorithm and propose a greedy randomized extended average block Kaczmarz algorithm (GREABK), and establish the global convergence theory of the GREABK algorithm. Finally, numerical experiments have shown that the GREABK algorithm outperforms the REABK algorithm in terms of iteration steps.