To overcome defects of conventional hybrid rockets such as low combustion efficiency and the O/F shift during the combustion, the authors have proposed a new form of hybrid rocket fuel. The fuel is a fibrous bed in which oxidizer gas flows. Stable diffusion flame appears at the exit surface. Previous researches show that sudden increase of the fuel regression rate occurs with the increase of ambient pressure. This sudden increase is attributed to the flame spreading between fuel fibers. To clarify the limit of fuel gap space the diffusion flame can spread into, experimental study was made. Critical gap space, which means the minimum gap space the diffusion flame can spread into, was obtained experimentally as a function of oxygen gas flow velocity and ambient pressure. Using this result, necessary conditions to realize a stable combustion with this new fuel form are shown.