The electronic structures and Kondo insulator state of the Pu monochalcogenides are computationally investigated, using the local density approximation (LDA), the LDA+U and dynamical mean field theory (LDA+DMFT) methods. We show that an enhanced hybridization of the Pu-5f state with the conduction bands occurs through the dynamical effect in the DMFT, which leads to the effective formation of a small energy gap around the Fermi level. Our LDA+DMFT calculations explain quantitatively the anomalous energy gap enhancement under pressure, observed for PuTe. The peculiar change of the energy gap of PuTe with pressure is found to result from a subtle crossover in the k-dispersion of the lowest excited states.