Among various kinds of methods for the stabilization of heavy metals in municipal solid waste incineration fly ash (MSWI FA), acid leaching is the most prevalent. However, the process of heavy metals leaching in MSWI FA by various acids must be compared. In this study, we extracted the heavy metals in MSWI FA using 0.5 M solutions of strong acids (HCl, H2SO4 and HNO3), as well as weak acids (NH4Cl, (NH4)2SO4 and NH4NO3). Solidification by CO2 injection occurred in all the leaching solutions. The leaching test was performed for solids such as treated MSWI FA and the precipitates produced in the solidification process, compared with untreated MSWI FA. The solids were analyzed by using X-Ray fluorescence spectroscopy, X-Ray diffraction, and scanning electron microscopy. The leaching solutions were analyzed by inductively coupled plasma-optical emission spectroscopy. Using weak acid solutions, Zn, Pb, and Cu were leached 15-70 times, two times, and 20-150 times, respectively, more than those leached strong acids. Except H2SO4 and (NH4)2SO4 solutions, all the acids reduced the mass of MSWI FA and extracted heavy metals. The crystalline precipitates were the carbonates. HNO3 solution was found to be the most appropriate solvent for the proposed method.