Summary: The existence of a positive periodic solution for \[ \begin{aligned} \frac{dH(t)}{dt}&= r(t)H(t) \left[1-\frac{H(t-\tau(t))}{K(t)}\right] -\alpha(t)H(t) P(t),\\ \frac{dP(t)}{dt}&= -b(t)P(t)+\beta(t)P(t)H(t-\sigma(t)), \end{aligned} \] is established, where \(r\), \(K\), \(\alpha\), \(b\), \(\beta\) are positive periodic continuous functions with period \(\omega>0\), and \(\tau\), \(\sigma\) are periodic continuous functions with period \(\omega\).