  For an odd prime $p$ and two positive integers $n\geq 3$ and $k$ with
$\frac{n}{{\rm gcd}(n,k)}$ being odd, the paper determines the weight
distribution of a $p$-ary cyclic code $\mathcal{C}$ over $\mathbb{F}_{p}$ with
nonzeros $\alpha^{-1}$, $\alpha^{-(p^k+1)}$ and $\alpha^{-(p^{3k}+1)}$, where
$\alpha$ is a primitive element of $\mathbb{F}_{p^n}$
