  We study the softcore extended Bose Hubbard model in a two-dimensional
triangular lattice by using the quantum Monte Carlo methods. The ground state
phase diagram of the system exhibits a very fruitful structure. Except the Mott
insulating state, four kinds of solid states with respect to the commensurate
filling factors $\rho=1/3,2/3$ and $\rho=1$ are identified. Two of them (CDW II
and CDW III) are newly predicted. In incommensurate fillings, superfluid,
spuersolid as well as phase separation states are detected . As in the case for
the hardcore bosons, a supersolid phase exists in $1/3<\rho<2/3$ while it is
unstable towards the phase separation in $\rho<1/3$. However, this instability
is refrained in $2/3<\rho<1$ due to the softening of the bosons and then a
supersolid phase survives.
