The accuracy of the immersed-boundary method is investigated for the simulation of the propagation of a premixed flame, characterized by sharp and moving interfaces separating unburned and burned gases with disparate fluid properties. In particular, the spurious pressure fields observed when employing the cosine weighting function in previous studies are found to be caused by the non-conservation in the interfacial region, and are removed in the present study by using area weighting. Furthermore, the sensitivity of the front propagation velocity to the movement and location of the flame, characterized by a discontinuous velocity profile, is substantially moderated by the use of an improved technique based on known immersion distribution. The improved performance of the present method is demonstrated through the evolution of the Darrieus-Landau instability.