  In this paper, we study the quantization of the (1+1)-dimensional projectable
Ho\v{r}ava-Lifshitz (HL) gravity, and find that, when only gravity is present,
the system can be quantized by following the canonical Dirac quantization, and
the corresponding wavefunction is normalizable for some orderings of the
operators. The corresponding Hamilton can also be written in terms of a simple
harmonic oscillator, whereby the quantization can be carried out quantum
mechanically in the standard way. When the HL gravity minimally couples to a
scalar field, the momentum constraint is solved explicitly in the case where
the fundamental variables are functions of time only. In this case, the coupled
system can also be quantized by following the Dirac process, and the
corresponding wavefunction is also normalizable for some particular orderings
of the operators. The Hamilton can be also written in terms of two interacting
harmonic oscillators. But, when the interaction is turned off, one of the
harmonic oscillators has positive energy, while the other has negative energy.
A remarkable feature is that orderings of the operators from a classical
Hamilton to a quantum mechanical one play a fundamental role in order for the
Wheeler-DeWitt equation to have nontrivial solutions. In addition, the
space-time is well quantized, even when it is classically singular.
