  Among various phenomenological $\Lambda$ models, a time-dependent model $\dot
\Lambda\sim H^3$ is selected here to investigate the $\Lambda$-CDM cosmology.
Using this model the expressions for the time-dependent equation of state
parameter $\omega$ and other physical parameters are derived. It is shown that
in $H^3$ model accelerated expansion of the Universe takes place at negative
energy density, but with a positive pressure. It has also been possible to
obtain the change of sign of the deceleration parameter $q$ during cosmic
evolution.
