In this work we investigate the weak $Lambda_{b}toLambda_c$ semi-leptonic and non-leptonic decays. The light-front quark model and diquark picture for heavy baryons are adopted to evaluate the $Lambda_{b}toLambda_c$ transition form factors. In the heavy quark limit we study the Isgur-Wise function. By fitting the data of the semi-leptonic process we obtain the mass of the light scalar diquark as 817 MeV. The numerical predictions on the branching ratios of non-leptonic decay modes $Lambda_{b}toLambda_c M$ and various polarization asymmetries are made. A comparison with other approaches is discussed.
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