Based on the construction of a new distance-preserving Gray map from ((Fp +uFp )N , Gray distance) to (the corresponding Gray images in FppN , Ham-ming distance) and the calculation of Gray distances of (u?1)-constacyclic codes over Fp +uFp , a bound for the Hamming distances of a class of negacyclic codes with length pN over Fp is obtained, which is more tighter than Singleton bound. Further more, the exact Hamming dis-tances of some p-ary negacyclic codes are determined from this bound, some of which cannot be got from Dinh's work published on Finite Fields and Their Applications in 2008.
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