  In this work we investigate the weak $\Lambda_{b}\to\Lambda_c$ semi-leptonic
and non-leptonic decays. The light-front quark model and diquark picture for
heavy baryons are adopted to evaluate the $\Lambda_{b}\to\Lambda_c$ 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 $\Lambda_{b}\to\Lambda_c M$ and various polarization
asymmetries are made. A comparison with other approaches is discussed.
