Hybrid flow shop scheduling (HFSP) is a frontier direction in the manufacture field, and it is of practical significance to study the problem with blocking constraints. Aiming at the blocking hybrid flow shop scheduling problem (BHFSP), this paper establishes the mathematical model of BHFSP with the objective of minimizing the makespan and describes its calculation process in detail. Based on the zero buffer characteristic, an iterative greedy algorithm with double level mutation (IGDLM) algorithm is designed to solve BHFSP. This paper analyzes the advantages and disadvantages of the traditional IG algorithm, and a double level mutation strategy based on the blocking characteristics is proposed to improve the diversity of the solution, balancing the global exploration and exploitation abilities of the proposed algorithm. The 100 test instances numerical simulations and statistical comparison with five representative algorithms show that the proposed algorithm integrating doule level into IG algorithm is able to get a better objective value, provide a better scheduling scheme for medium and large-scale BHFSP than the compared algorithms.