  A class of generalized Verma modules over $\fr{sl}_{n+2}$ is constructed from
$\fr{sl}_{n+1}$-modules which are $\uhn$-free modules of rank $1$. The
necessary and sufficient conditions for these $\fr{sl}_{n+2}$-modules to be
simple are determined. This leads to a class of new simple
$\fr{sl}_{n+2}$-modules.
