Abstract: Compared with cross-cloud data center replication, cross-cloud data center erasure code is more reliable and space-efficiency. However, existing cross-cloud data center erasure codes cannot achieve low cross-cloud data center repair traffic, high encoding parameters adaptability, and high erasure code construction efficiency at the same time, so they are rarely used in production. We propose a fast construction method of the erasure code with small cross-cloud data center repair traffic, called FMEL, which can obtain the erasure code with small cross-cloud data center repair traffic quickly under different encoding parameters. Specifically, FMEL converts erasure code repair group distribution schemes and the corresponding encoding parameters into fixed-length feature vectors, and verifies whether the erasure code repair group distribution schemes match the encoding parameter by classifying corresponding feature vectors with a support vector machine—a feature vector positively indicates that the corresponding erasure code repair group distribution scheme passes the verification. Then, FMEL uses a parallel search algorithm to pick the erasure code repair group distribution scheme with the smallest cross-cloud data center repair traffic from all distribution schemes passing the verification, and converts it into the generator matrix of the erasure code with small cross-cloud data center repair traffic. Experiments in a cross-cloud data center environment show that FMEL can construct the optimal code that can achieve the lower bound of cross-cloud data center repair traffic under most encoding parameters. Meanwhile, FMEL’s erasure code construction time is 89% less than the existing work’s optimal code construction time. Compared with several popular erasure codes, the erasure code constructed by FMEL can reduce the cross-cloud data center repair traffic by from 42.9% to 56.0%.