The propagation effect in an open V-type three-level atomic system with spontaneously generated coherence is studied by numerical calculation. The results show that changing the relative phase between the probe and driving field has an important effect on variations of gain and intensity of lasing without inversion (LWI) with propagation distance, i.e. spatial evolution; variation of ratio (S) between the atomic injection rate and atomic exit rate (r0) has a remarkable modulation role in phase-dependent spatial evolution. In a certain range of S (r0), with value of S (r0) increasing, LWI gain and intensity increase and the propagation distance needed for reaching an intensity maximum value becomes longer; In a corresponding closed system, the maxima of LWI gain, intensity and the propagation distance along which the gain can be produced are smaller than in an open system. The Doppler effect also has an obvious influence on spatial evolutions of LWI gain and intensity, values of LWI gain and intensity are smaller in the presence of Doppler effect than in the absence of Doppler effect.