  A scale-free network is grown in the Euclidean space with a global
directional bias. On a vertical plane, nodes are introduced at unit rate at
randomly selected points and a node is allowed to be connected only to the
subset of nodes which are below it using the attachment probability: $\pi_i(t)
\sim k_i(t)\ell^{\alpha}$. Our numerical results indicate that the directed
scale-free network for $\alpha=0$ belongs to a different universality class
compared to the isotropic scale-free network. For $\alpha < \alpha_c$ the
degree distribution is stretched exponential in general which takes a pure
exponential form in the limit of $\alpha \to -\infty$. The link length
distribution is calculated analytically for all values of $\alpha$.
