  The $\Lambda$CDM model is a remarkably successful model which is consistent
with the observations of cosmic microwave background radiation (CMB), baryon
acoustic oscillation (BAO), and large scale structure of the Universe. However,
the discrepancy in the value of $H_0$ between the local observations and PLANCK
observation of CMB was recently pointed out. One of the way to ease the
discrepancy is to introduce phantom dark energy instead of the cosmological
constant. While, phantom dark energy often suffer from the instabilities. We
will investigate the general solution to overcome the difficulty of phantom
dark energy and construct some particular models which have a phantom crossing
and can be consistent with the observations.
