The modulation instability evolving from a continuously amplitude‐modulated perturbation is observed in the ionization waves excited in the He positive column of a glow discharge. The degree of modulation increases with wave propagation, and an isolated pulse‐like wave evolves. The so‐called envelope soliton propagates toward the anode, retaining its own waveform. The measured growth rate of the modulational instability agrees well with that of the calculated one. The growth rate becomes maximum at a certain modulation frequency, as is predicted by a coupled mode theory.