In this work, we analyze the semileptonic decay processes of $$\varLambda _b \rightarrow \varLambda _c$$ ${\Lambda }_b\to {\Lambda }_c$ in the light-cone sum rule approach. In order to calculate the form factors of the $$\varLambda _b$$ ${\Lambda }_b$ baryon transition matrix element, we use the light-cone distribution amplitudes of $$\varLambda _b$$ ${\Lambda }_b$ obtained from the QCD sum rule in the heavy quark effective field theory framework. With the calculation of the six form factors of the $$\varLambda _b \rightarrow \varLambda _c$$ ${\Lambda }_b\to {\Lambda }_c$ transition matrix element, the differential decay widths of $$\varLambda _b^0 \rightarrow \varLambda _c^+ \ell ^- {\overline{\nu }}_\ell (\ell = e, ~\mu , ~\tau )$$ ${\Lambda }_b^0\to {\Lambda }_c^{+}{\ell }^{-}{\overline{\nu }}_{\ell }(\ell =e,\mu ,\tau )$ and their absolute branching fractions are obtained. Additionally, the ratio of $$R(\varLambda _c^+) \equiv {\mathcal {B}}r(\varLambda _b^0 \rightarrow \varLambda _c^+ \tau ^- {\overline{\nu }}_\tau )/{\mathcal {B}}r(\varLambda _b^0 \rightarrow \varLambda _c^+ \mu ^- {\overline{\nu }}_\mu )$$ $R\left({\Lambda }_c^{+}\right)\equiv Br({\Lambda }_b^0\to {\Lambda }_c^{+}{\tau }^{-}{\overline{\nu }}_{\tau })/Br({\Lambda }_b^0\to {\Lambda }_c^{+}{\mu }^{-}{\overline{\nu }}_{\mu })$ is also obtained in this work. Our results are in accord with the newest experimental result and other theoretical calculations and predictions.