For an odd prime p which is congruent to 3 module 4 and an odd integer k, we investigate the upper bound on the magnitude of cross correlation values of a p-ary m-sequence s(t) and its decimated sequences s(dt + l) for a decimation value d. Using the above upper bound of the magnitude of cross correlation values of pary m-sequence and its decimated sequences, we construct a new class of p-ary sequence families with low correlation property via m-sequence.