  The semileptonic transition of $\Lambda_b$ baryon is studied using the
Hypercentral constituent quark model. The six-dimensional hyperradial
$Schr\ddot{o}dinger$ equation is solved in the variational approach to get
masses and wavefunctions of heavy baryons. The matrix elements of weak decay
are written in terms of the overlap integrals of the baryon wave function. The
Isgur-Wise function is determined to calculate exclusive semileptonic decay
$\Lambda_b$ $\rightarrow$ $\Lambda_c$ $\ell$ $\bar{\nu}$. The calculated decay
rate and the branching ratio of $\Lambda_b$ baryon are consistent with other
theoretical predictions and with the available experimental observations.
