  The statistical properties of mostly expanding partially hyperbolic
diffeomorphisms have been substantially studied. In this paper, we would like
to address the entropy properties of mostly expanding partially hyperbolic
diffeomorphisms. We prove that for mostly expanding partially hyperbolic
diffeomorphisms with minimal strong stable foliation and one-dimensional center
bundle, there exists a $C^1$-open neighborhood of them, in which the
topological entropy varies continuously and the intermediate entropy property
holds. To prove that, we show that each non-hyperbolic ergodic measure is
approached by horseshoes in entropy and in weak$*$-topology.
