Solitary waves of the fast beam mode in a positive ion-beam and a quasi-neutral three-component plasma system are investigated theoretically and experimentally. The plasma is assumed to be composed of electrons, positive ions and negative ions. When the concentration r of the negative ions is larger than a critical value, a small rarefactive (negative) soliton propagates instead of a compressive (positive) one. When the beam is injected into the plasma, the ion-acoustic wave gradually converts to the fast beam mode. The rarefactive soliton exists when the beam velocity is less than or equal to a threshold value and a compressive soliton exists when the beam velocity is greater than the threshold value. The threshold beam velocity is measured as a function of r and is compared with the theoretical prediction.