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This paper is devoted to investigate the existence of positive periodic solution for a functional differential equation in the form of $\lambda\mathbb{L}x=-b(t)f(x(t-\tau(t))),$ where $\mathbb{L}x=x'(t)-a(t)g(x(t))x(t)$. By using well-known fixed point index theory in a cone, values of $\lambda$ are determined for which there exist positive periodic solutions for the above functional differential equation. The dependence of positive periodic solution $x_{\lambda}(t)$ on the parameter $\lambda$ is also studied, i.e., $$\lim\limits_{\lambda\rightarrow+\infty}\|x_{\lambda}\|=+\infty\quad or\quad \lim\limits_{\lambda\rightarrow+\infty}\|x_{\lambda}\|=0.$$