  In this paper, for an odd prime $p$, several classes of two-weight linear
codes over the finite field $\mathbb{F}_p$ are constructed from the defining
sets, and then their complete weight distributions are determined by employing
character sums. These codes can be suitable for applications in secret sharing
schemes. Furthermore, two new classes of projective two-weight codes are
obtained, and then two new classes of strongly regular graphs are given.
