For dealing with the processing time uncertainty widely existing in the real-world production process, this paper uses fuzzy number to represent each job's processing time, and establishes a model of the green distributed permutation flow-shop scheduling problem with fuzzy processing time(GDPFSP_FPT), whose optimization objectives are the fuzzy maximum completion time and the fuzzy total energy consumption. The, a hyper-heuristic cross-entropy algorithm(HHCE) is proposed for solving the GDPFSP_FPT. Firstly, the HHCE algorithm adopts a novel ranking rule of triangular fuzzy number to reasonably calculate the objective function values of individuals, which is helpful in finding the promsing regions more accurately during the search process. Secondly, in the upper layer, the HHCE algorithm utilizes an evaluation method based on the contribution rate to estimate the permutations constructed by eight special neighbor operations, and also uses the cross-entropy(CE) method to learn the information of better permutations and generate new permutations. Then, for searching more different regions in solution space, the algorithm uses each permutation generated in the upper layer as a heuristic to perform a series of neighbor operations on the corresponding individuals in the lower layer. Thirdly, in order to enhence its ability of obtaining the non-dominated individuals or solutions with low energy consumption, the algorithm utilizes an energy-saving strategy based on non-critical path to perform local search on better individuals of each generation. Finally, simulations and comparisons demonstrate that the HHCE algorithm can effectively solve the GDPFSP_FPT.