Abstract: The existence and location of conjugate points along null geodesics in Taub's vacuum spacetime is investigated in detail. It is shown that every null geodesic $\eta$ not confined in a t-z plane contains two pairs of segments ($\mathcal{M}$, $\widetilde{\mathcal{M}}$) and ($\mathcal{N}$ $\widetilde{\mathcal{N}}$) such that each point p in $\mathcal{M}$(resp.$\mathcal{N}$) has a unique conjugate point $\widetilde{p}$ along $\eta$ that is located in $\widetilde{\mathcal{M}}$ (resp. $\widetilde{\mathcal{N}}$) and vice versa, and what is more interesting, if p and $\widetilde{\mathcal{p}}$ are conjugate points along $\eta$ with $\widetilde{\mathcal{p}}$∈J⁺(p), then $\widetilde{\mathcal{p}}$∈I⁺(p). This presents a realistic example illustrating that there do exist null geodesics emanating from p that can get into I⁺(p) before meeting a point conjugate to p. All results are generalized to a class of spacetimes.