  We present the analysis of exclusive $0^{-}$$\to$$0^{-}$ semileptonic heavy
meson decays using the constituent quark model based on the light-front
quantization. Our model is constrained by the variational principle for the
well-known linear plus Coulomb interaction motivated by QCD. Our method of
analytic continuation to obtain the weak form factors avoids the difficulty
associated with the contribution from the nonvalence quark-antiquark pair
creation. Our numerical results for the heavy-to-heavy and heavy-to-light meson
decays are in a good agreement with the available experimental data and the
lattice QCD results. In addition, our model predicts the two unmeasured mass
spectra of $^{1}S_{0}(b\bar{b})$ and $^{3}S_{1}(b\bar{s})$ systems as
$M_{b\bar{b}}$=9657 MeV and $M_{b\bar{s}}$= 5424 MeV.
