  We study an extended Bose-Hubbard model with next-nearest-neighbor (NNN)
hopping in a shaken optical lattice. We show how mean-field phase diagram
evolves with the change of NNN hopping amplitude $t_{2}$, which can be easily
tuned via shaking amplitude. As $t_{2}$ increases, a $Z_{2}$-symmetry-breaking
superfluid ($Z_{2}$SF) phase emerges at the bottom of the Mott lobs. The
tricritical points between normal superfluid, $Z_{2}$SF, and Mott insulator
(MI) phases are identified. We further demonstrate the tricritical point can be
tuned to the tip of the Mott lobe, in which case a new critical behavior has
been predicted. Within random-phase approximation, excitation spectra in the
three phases are obtained, which indicate how the phase transitions occur.
