  Linear codes have been an interesting topic in both theory and practice for
many years. In this paper, for an odd prime $p$, we present the explicit
complete weight enumerator of a family of $p$-ary linear codes constructed with
defining set. The weight enumerator is an mmediate result of the complete
weight enumerator, which shows that the codes proposed in this paper are
three-weight linear codes. Additionally, all nonzero codewords are minimal and
thus they are suitable for secret sharing.
