We investigated the low-temperature processed polycrystalline-silicon (poly-Si) film formed by carrying out low-energy-density and multishot excimer laser annealing (ELA) of amorphous Si (a-Si) film on a glass or quartz substrate. The influence of secondary grain growth which grain size becomes larger than the film thickness on the tensile stress relaxation of the poly-Si film was clarified. Relationship between hydrogens which are supplied to the melt-Si from the bottom catalytic-chemical vapor deposition (Cat-CVD) SiN film and the stress relaxation was also examined. The tensile stress in the poly-Si film relaxes upon the appearance of the secondary grains, and the stress decreases with increasing diameter of the secondary grains. However, the hydrogen supply to melt-Si suppresses the secondary grain growth and the stress relaxation becomes marked as the hydrogen concentration decreases. Furthermore, the relationship between the dangling bond density corresponding to the crystal defect density and grain size was investigated, and the defect site was clarified. Lastly, the recrystallization model by ELA at low energy densities was discussed. The model was constructed based on the experimental data that the secondary grain growth occurs suddenly at the critical energy density and the critical shot number, and it was shown that the present model is consistent with the results related to the hydrogen concentration and the secondary grain growth.