$Lambda^+_c$- and $Lambda_b$-hypernuclei are studied in the quark-meson coupling (QMC) model. Comparisons are made with the results for $Lambda$-hypernuclei studied in the same model previously. Although the scalar and vector potentials felt by the $Lambda$, $Lambda_c^+$ and $Lambda_b$ in the corresponding hypernuclei multiplet which has the same baryon numbers are quite similar, the wave functions obtained, e.g., for $1s_{1/2}$ state, are very different. The $Lambda^+_c$ baryon density distribution in $^{209}_{Lambda^+_c}$Pb is much more pushed away from the center than that for the $Lambda$ in $^{209}_Lambda$Pb due to the Coulomb force. On the contrary, the $Lambda_b$ baryon density distributions in $Lambda_b$-hypernuclei are much larger near the origin than those for the $Lambda$ in the corresponding $Lambda$-hypernuclei due to its heavy mass. It is also found that level spacing for the $Lambda_b$ single-particle energies is much smaller than that for the $Lambda$ and $Lambda^+_c$.
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