In cross-datacenter storage systems, existing writing methods of erasure code usually has low encoding efficiency, low transmission efficiency, and large network resource consumption. Therefore, cross-datacenters erasure code usually has a low writing rate. This paper proposes a cross-datacenter erasure code writing method based on generator matrix transformation called CREW. Specifically, we first propose a greedy strategy-based transmission topology construction algorithm called GBTC, which can construct a tree-structured transmission topology with incremental weights (the weights are set to the network distances between datacenters) from top to bottom to organize data transmission between datacenters. Then, we propose a generator matrix transformation algorithm called GMT. Without changing the linear relationship of coded blocks, GMT can transform the generator matrix so that the number of data blocks related to a coded block is negatively correlated with the network distance between the datacenter where the coded block is located and the root of the tree-structured topology. Therefore, CREW only needs to transfer a small number of data blocks through a long network distance to write data. Thus, the network resource consumption is reduced. Finally, we propose a distributed pipelined writing algorithm called DPW to distribute encoding operations to different nodes for parallel execution and limit the number of forwards of data blocks, thereby improving encoding efficiency and transmission efficiency. Experiments show that compared with writing methods of traditional erasure code, the write rate of CREW is increased by 36.3%~57.9%. And compared with the existing writing method of cross-datacenter erasure code (IncEncoding), the writing rate of CREW is increased by 32.4%.