  We present the global phase diagram of the extended boson Hubbard model on a
simple cubic lattice by quantum Monte Carlo simulation with worm update
algorithm. Four kinds of phases are supported by this model, including
superfluid, supersolid, Mott, and charge density wave (CDW) states, which are
identified in the phase diagram of chemical potential $\mu$ versus nearest
neighbor interaction V . By changing the chemical potential, a continuous
transition is found from the Mott phase to a superfluid phase without breaking
the translational symmetry. For an insulating CDW state, adding particles to it
gives rise to a continuous transition to a supersolid phase, while removing
particles usually leads to a first-order one to either supersolid or superfluid
phase. By tuning the nearest neighbor interaction, one can realize the
transition between two insulating phases, Mott and CDW with the same particle
density, which turns out to be of the first-order. We also demonstrate that a
supersolid phase with average particle density less than 1/2 can exist in a
small region of $\mu$ - V phase diagram.
