Predissociation of H-3 Rydberg states was investigated using the effective Hamiltonian which describes the vibronic transitions among the Rydberg states as well as the predissociation through the vibrationally excited 2s states. The motion of a Rydberg electron and the vibrations of the H-3(+) ion core was treated simultaneously without assuming the Born-Oppenheimer approximation. We developed the effective potential for a Rydberg electron, which contains the Coulomb potential and the exchange effect. The energies and predissociation lifetimes of H-3 Rydberg states were obtained by analyzing the effective Hamiltonian and compared with the available experimental values. The s and p Rydberg states with lower vibrational excitation have lifetimes between a few ps to 1 ns and show an irregular lifetime distribution with respect to the principal quantum number. In contrast, d and f Rydberg states have longer lifetime, 10 ns for example. The energy level spacings of the Rydberg states obey the distribution close to the Poisson one and thus indicates these states being regular. The route of predissociation was investigated by propagating a wave packet as well as analyzing the eigenvectors of the effective Hamiltonian. We found that the energy level matching between nearby states play an important role for efficient predissociation. The present results suggest that the predissociation of the H-3 molecule and the dissociative recombination of the H-3(+) ion might be efficient under rotational excitation through inclusion of additional energy levels.