  The electronic property and magnetic susceptibility of Ce$_3$Pd$_3$Bi$_4$
were systemically investigated from 18 K to 290 K for varying values of
cell-volume using dynamic mean-field theory coupled with density functional
theory. By extrapolating to zero temperature, the ground state of
Ce$_3$Pd$_3$Bi$_4$ at ambient pressure is found to be a correlated semimetal
due to insufficient hybridization. Upon applying pressure, the hybridization
strength increases and a crossover to Kondo insulator is observed at finite
temperatures. The characteristic temperature signaling the formation of Kondo
singlet, as well as the characteristic temperature associated with $f$-electron
delocalization-localization change, simultaneously vanishes around a critical
volume of 0.992$V_0$, suggesting that such metal-insulator transition is
possibly associated with a quantum critical point. Finally, the Wilson's loop
calculations indicate that the Kondo insulating side is topologically trivial,
thus a topological transition also occurs across the quantum critical point.
