In this paper, a family of cyclic codes over Fp\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${\mathbb {F}}_{p}$$\end{document} whose duals have five zeros is presented, where p is an odd prime. Furthermore, the weight distribution of these cyclic codes is determined.