We derive the master equation of a double quantum dot charge qubit by taking into account the dissipative effects of the phonon-bath environment, and study the current noise spectrum of the double quantum dot charge qubit in terms of full counting statistics. It is found that the current is asymmetric about the current peak. The Fano factor displays an asymmetric double-peak structure, the asymmetry is due to the dissipations induced by the phonon bath. With increasing temperature T of the phonon bath, the current resonance broadens, the Fano factor peaks become smaller, and the super-Poissonian behavior vanishes.