  Assume $n, m$ are positive integers and $G$ is a graph. Let $P_{n,m}$ be the
graph obtained from the path with vertices $\{-m, -(m-1), \ldots, 0, \ldots,
n\}$ by adding a loop at vertex $ 0$. The double cone $\Delta_{n,m}(G)$ over a
graph $G$ is obtained from the direct product $G \times P_{n,m}$ by identifying
$V(G) \times \{n\}$ into a single vertex $(\star, n)$, identifying $V(G) \times
\{-m\}$ into a single vertex $(\star, -m)$, and adding an edge connecting
$(\star, -m)$ and $(\star, n)$. This paper determines the fractional chromatic
number of $\Delta_{n,m}(G)$. In particular, if $n < m$ or $n=m$ is even, then
$\chi_f(\Delta_{n,m}(G)) = \chi_f(\Delta_n(G))$, where $\Delta_n(G)$ is the
$n$th cone over $G$. If $n=m$ is odd, then $\chi_f(\Delta_{n,m}(G)) >
\chi_f(\Delta_n(G))$. The chromatic number of $\Delta_{n,m}(G)$ is also
discussed.
