The monogamy of entanglement is an important property in quantum entanglement, which can be used to characterize the entanglement structure in multipartite systems. Tsallis-q entropy entanglement is a well-known entanglement measure, and the squared Tsallis-q entropy entanglement obeys a monogamy relation with 5－132≤q≤5+132. A new entanglement monogamy relation is presented when the μ-th power of Tsallis-q entropy entanglement with 5－132≤q≤5+132 is satisfied with μ≥2. It is shown that this monogamy relation is more strict than the monogamy relation of squared Tsallis-q entropy entanglement proposed by Song et al.