  We obtain a general spherically symmetric solution of a null dust fluid in $n
(\geq 4)$-dimensions in Gauss-Bonnet gravity. This solution is a generalization
of the $n$-dimensional Vaidya-(anti)de Sitter solution in general relativity.
For $n=4$, the Gauss-Bonnet term in the action does not contribute to the field
equations, so that the solution coincides with the Vaidya-(anti)de Sitter
solution. Using the solution for $n \ge 5$ with a specific form of the mass
function, 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 and its properties are quite
different between $n=5$ and $n \ge 6$. In the $n \ge 6$ case, a massless
ingoing null naked singularity is formed, while in the $n=5$ case, a massive
timelike naked singularity is formed, which does not appear in the general
relativistic case. The strength of the naked singularities is weaker than that
in the general relativistic case. These naked singularities can be globally
naked when the null dust fluid is turned off after a finite time and the field
settles into the empty asymptotically flat spacetime.
