  In this paper, we introduce the $n$-dimensional Lorentzian wormhole solutions
of third order Lovelock gravity. In contrast to Einstein gravity and as in the
case of Gauss-Bonnet gravity, we find that the wormhole throat radius, $r_0$,
has a lower limit that depends on the Lovelock coefficients, the dimensionality
of the spacetime and the shape function. We study the conditions of having
normal matter near the throat, and find that the matter near the throat can be
normal for the region $r_0 \leq r \leq r_{\max}$, where $r_{\max}$ depends on
the Lovelock coefficients and the shape function. We also find that the third
order Lovelock term with negative coupling constant enlarges the radius of the
region of normal matter, and conclude that the higher order Lovelock terms with
negative coupling constants enlarge the region of normal matter near the
throat.
