  In this work, a minisuperspace model for the projectable Ho\v{r}ava-Lifshitz
(HL) gravity without the detailed balance condition is investigated. The
Wheeler-deWitt equation is derived and its solutions are studied and discussed
for some particular cases where, due to HL gravity, there is a "potential
barrier" nearby $a=0$. For a vanishing cosmological constant, it is found a
normalizable wave function of the universe. When the cosmological constant is
non-vanishing, the WKB method is used to obtain solutions for the wave function
of the universe. Using the Hamilton-Jacobi equation, one discusses how the
transition from quantum to classical regime occurs and, for the case of a
positive cosmological constant, the scale factor is shown to grow
exponentially, hence recovering the GR behaviour for the late universe.
