The phases of high-entropy alloys (HEAs) are crucial to their material properties. Although meta-learning can recommend a desirable algorithm for materials designers, it does not utilize the optimal solution information of similar historical problems in the HEA field. To address this issue, a transferable meta-learning model (MTL-AMWO) based on an adaptive migration walrus optimizer is proposed to predict the phases of HEAs. Firstly, a transferable meta-learning algorithm frame is proposed, which consists of meta-learning based on adaptive migration walrus optimizer, balanced-relative density peaks clustering, and transfer strategy. Secondly, an adaptive migration walrus optimizer model is proposed, which adaptively migrates walruses according to the changes in the average fitness value of the population over multiple iterations. Thirdly, balanced-relative density peaks clustering is proposed to cluster the samples in the source and target domains into several clusters with similar distributions, respectively. Finally, the transfer strategy adopts the maximum mean discrepancy to find the most matching historical problem and transfer its optimal solution information to the target domain. The effectiveness of MTL-AMWO is validated on 986 samples from six datasets, including 323 quinary HEAs, 366 senary HEAs, and 297 septenary HEAs. The experimental results show that the MTL-AMWO achieves better performance than other algorithms.