  We discuss the Picard group of moduli space $\mathcal{K}_g$ of
quasi-polarized K3 surfaces of genus $g\leq 12$ and $g\neq 11$. In this range,
$\mathcal{K}_g$ is unirational and a general element in $\mathcal{K}_g$ is a
complete intersection with respect to a vector bundle on a homogenous space, by
the work of Mukai. In this paper, we find generators of the Picard group
$Pic_\mathbb{Q}(\mathcal{K}_g)$ using Noether-Lefschetz theory. This verifies
the Noether-Lefschetz conjecture on moduli of K3 surfaces in these cases.
