  Draco dwarf Spheroidal galaxy (dSph) is one of the nearest and the most dark
matter dominated satellites of the Milky Way. We obtained multi-epoch
near-infrared (NIR, $JHK_s$) observations of the central region of Draco dSph
covering a sky area of $\sim 21'\times21'$ using the WIRCam instrument at the
3.6-m Canada-France-Hawaii Telescope. Homogeneous $JHK_s$ time-series
photometry for 212 RR Lyrae (173 fundamental-mode, 24 first-overtone, and 15
mixed-mode variables) and 5 Anomalous Cepheids in Draco dSph is presented and
used to derive their period-luminosity relations at NIR wavelengths for the
first-time. The small scatter of $\sim 0.05$~mag in these empirical relations
for RR Lyrae stars is consistent with those in globular clusters and suggests a
very small metallicity spread, up to $\sim0.2$~dex, among these centrally
located variables. Based on empirically calibrated NIR
period-luminosity-metallicity relations for RR Lyrae in globular clusters, we
determined a distance modulus to Draco dSph of $\mu_\textrm{RRL} = 19.557 \pm
0.026$ mag. The calibrated $K_s$-band period-luminosity relations for Anomalous
Cepheids in the Draco dSph and the Large Magellanic Cloud exhibit statistically
consistent slopes but systematically different zero-points, hinting at possible
metallicity dependence of $\sim-0.3$ mag~dex$^{-1}$. Finally, the apparent
magnitudes of the tip of the red giant branch in $I$ and $J$ bands also agree
well with their absolute calibrations with the adopted RR Lyrae distance to
Draco. Our recommended $\sim1.5\%$ precise RR Lyrae distance, $D_\textrm{Draco}
= 81.55 \pm 0.98 \textrm{(statistical)} \pm 1.17 \textrm{(systematic)}$~kpc, is
the most accurate and precise distance to Draco dSph galaxy.
