Propagation effects of lasing without inversion(LWI)in a Doppler-broadened open four-level system are studied and simulated numerically. The results of numerical calculation for theoretical equations with considering propagation effect and Doppler effect in the open LWI system show that: 1)It is more advantageous to obtain LWI in the open system when the probing and driving fields are copropagating. 2)It is necessary for raising the probe gain that not only the driving field intensity at the entrance of the active medium needs be selected a proper value,but also the nominal detunings of driving and probe fields need be given suitable values. 3)With propagation length increase,population inversion cannot happen always in the upper and lower levels of the probed transition,and Raman inversion can be achieved in the upper level of the probed transition and upper level of optical transition which an intense external field drives.