  We have improved our previous variational method based constituent quark
model by introducing a complete set of 3-dimensional harmonic oscillator bases
as the spatial part of the total wave function. To assess the validity of our
approach, we compared the binding energy, thus calculated with the exact value
for the hydrogen model. After fitting to the masses of the ground state
hadrons, we apply our new method to analyze the doubly-heavy tetraquark states
$qq'\bar{Q}\bar{Q'}$ and compared the result for the binding energies with that
from other works. We also calculated the ground state masses of $T_{sc}
(ud\bar{s}\bar{c})$ and $T_{sb} (ud\bar{s}\bar{b})$ with $(I,S) = (0,1),
(0,2)$. We found that $T_{bb} (ud\bar{b}\bar{b})$ and $us\bar{b}\bar{b}$, both
with $(I,S) = (0,1)$, are stable against the two lowest threshold meson states
with binding energies $-145$ MeV and $-42$ MeV, respectively. We further found
that $T_{cb} (ud\bar{c}\bar{b})$ is near the lowest threshold. The spatial
sizes for the tetraquarks are also discussed.
