We prove a new polygamy relation of multi-party quantum entanglement in terms of R{e}nyi-$alpha$ entanglement of assistance for $left( {sqrt 7 - 1} right)/2leqalpha leq left( {sqrt 13 - 1} right)/2$. This class of polygamy inequality reduces to the polygamy inequality based on entanglement of assistance since R{e}nyi-$alpha$ entanglement is a generalization of entanglement of formation. We further show that the polygamy inequality also holds for the $mu$th power of R{e}nyi-$alpha$ entanglement of assistance.
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