The low energy electronic structure of LaFeAsO1-xHx (0.0 < x < 0.60), the system which exhibits two superconducting domes in its phase diagram, is investigated by utilizing the laser photoemission spectroscopy. From the precise temperature-dependent measurement of the spectra near the Fermi level, we find the suppression of the density of states with cooling, namely the pseudogap formation, for all doping range. The pseudogap in the low x range (i.e. the first superconducting dome regime) gets suppressed with increasing x, more or less similarly to the previous results in F-doped LaFeAsO system. On the other hand, the pseudogap behavior in the second superconducting dome regime at high-x becomes stronger with increasing the H-doping level. The systematic doping dependence shows that the pseudogap is enhanced toward the both ends of the phase diagram where the different types of antiferromagnetic order exist.