The nonlinear instability of an one-dimensional detonation wave was numerically simulated in the mixture of C₂H₆ and air with equivalence of 1. The influence of mesh size on the numerical results of pulsating of shock history was analyzed. Mesh size in calculation was fixed in according to the length of induction zone L_in, which was determined from ZND model to be 4.6 mm for the detonation wave in the mixture of C₂H₆ and air. As the decrease of mesh size, the solutions of pressure history do not tend to be identical. Detonation shock history was very irregular as the mesh size was not fine enough. As the mesh size was 0.01L_in and 0.005L_in, pulsating was regular with the mode of period-doubling mode. As the mesh size was 0.0025L_in, pulsating consisted of a series of regular oscillations and three irregular oscillations in the range of calculation, but finally the average wavelength of oscillations tended to 91~93 mm which approaches to the length of cell size of 88 mm from the experiments.