  In this paper, we present an exact spherically symmetric solution of third
order Lovelock gravity in $n$ dimensions which describes the gravitational
collapse of a null dust fluid. This solution is asymptotically (anti-)de Sitter
or flat depending on the choice of the cosmological constant. Using the
asymptotically flat solution for $n \geq 7$ with a power-law form of the mass
as a function of the null coordinate, we present a model for a gravitational
collapse in which a null dust fluid radially injects into an initially flat and
empty region. It is found that a naked singularity is inevitably formed whose
strength is different for the $n = 7$ and $n \geq 8$ cases. In the $n=7$ case,
the limiting focusing condition for the strength of curvature singularity is
satisfied. But for $n \geq 8$, the strength of curvature singularity depends on
the rate of increase of mass of the spacetime. These considerations show that
the third order Lovelock term weakens the strength of the curvature
singularity.
