Marginal detonation dynamics in a rectangular tube was numerically analyzed in this paper. The detailed chemical reaction model was employed to describe the heat release of detonation chemical reactions. The 2nd additive semi-implicit Runge-Kutta method and 5th order Weighted Essentially Non-Oscillatory (WENO) scheme were used to integrate the two-dimensional time-dependent reactive Euler equations. For the stoichiometric hydrogen and oxygen mixture diluted by 25% argon, as the channel width is 30 mm and the initial temperature is 300 K, the critical initial pressure for marginal detonation is 3.5 kPa. Under this critical condition, the cellular pattern, the velocity and maximum pressure along the wall and the wave evolution of marginal detonation were obtained. The difference between the marginal and ordinary detonation was discussed including the detonation velocity, average velocity, the ratio of cell width to length, transverse wave structure, unreacted gas pocket and vortex structure. The intrinsic instability and chemical dynamics characteristics of marginal detonation were deeply recognized.