In this paper, for an odd prime and an integer , a new family of -ary sequences of period with low correlation is constructed. The new family is constructed by shifts and additions of two decimated sequences of a -ary -sequence, and its family size is . The complete correlation distribution of this new family is derived. It is also shown that the family is optimal with respect to the parameter , which denotes the root mean square of all nontrivial correlations. Compared with the known sequence families, our sequence family is new and has a larger family size, which is four times of its period.