  Let Vect($\mathbb{R}$) be the Lie algebra of smooth vector fields on
$\mathbb{R}$ and $\mathbb{F}_{\lambda}$ be the space of $\lambda$-densities on
$\mathbb{R}$.
  Vect($\mathbb{R}$) acts on $\mathbb{F}_{\lambda}$ by Lie derivative. In this
paper, we compute the third differential cohomology of the Lie algebra
Vect($\mathbb{R}$) with coeffcients in the space $\mathbb{F}_{\lambda}.$
Explicit cocycles spanning these cohomology spaces are given.
