ABSTRACT The effects of unburned-gas temperature and pressure on the unstable behavior of cellular-flame fronts in hydrogen-air lean premixed flames are elucidated by numerical simulations. The detailed chemical reaction mechanism with seventeen reversible reactions of eight reactive species and a diluent is adopted for hydrogen-air combustion and heat loss is taken into account. The burning velocity of a planar flame increases as the unburned-gas temperature increases, and it decreases as the unburned-gas pressure and heat loss increase. In the dispersion relation, the growth rate increases and the unstable range widens when the unburned-gas temperature increases. The former decreases and the later narrows when the heat loss becomes larger. The normalized growth rates become large under the non-adiabatic conditions. The normalized burning velocity of a cellular flame is large when the pressure is high and heat loss is large, and it decreases as the temperature increases at high pressure. This shows that the high unburned-gas temperature at high pressure weakens the instability in hydrogen-air lean premixed flames. With increasing the domain size, the burning velocity of a cellular flame increases, and the cellular-flame front becomes more unbalance. This is an aspect of the long-wavelength disturbance to the unstable behavior of cellular-flame front.