  In this work, motivated by the energy bound suggested by Cohen {\it et al.},
we propose the modified holographic dark energy (MHDE) model. Choosing the IR
cut-off $L=R_{\rm CC}$ and considering the parameterizations $n^2=2-\lambda a$,
$n^2=2-3\lambda a^2/(1+3a^2)$ and $n^2=2-\lambda a^2/(\beta+a^2)$, we derive
all the physical quantities of the non-saturated MHDE model analytically. We
find that the non-saturated MHDE models with the parameterizations
$n^2=2-\lambda a$ and $n^2=2-3\lambda a^2/(1+3a^2)$ are single-parameter models
in practice. Also, we consider the cosmological constraints on the
non-saturated MHDE, and find that it is well consistent with the observational
data.
