During the diagenesis of many carbonate rocks, seawater rich in magnesium ions penetrates into the sediments and forms dolomite by replacement reactions with calcium ions in calcite. Different degrees of penetration and reaction lead to the formation of the dolomitized carbonate reservoirs, which has an impact on the acid dissolution mechanism. Current models only consider the calcite in carbonate rocks or mainly focus on the effect of average mineral content on the dissolution patterns, ignoring the effect of different mineral distributions. In this study, numerical simulations are carried out under different mineral distribution types and flow rates based on the extended two-scale continuum model applicable to acid dissolution in dolomitized carbonate reservoirs, which can provide theoretical guidance value for realizing the precise design of the acid treatment scheme in such reservoirs. The breakthrough volume and dissolution pattern are obtained from the time and porosity distribution during acid breakthrough, respectively. The results show that the mineral distribution in dolomitized carbonate reservoirs does not change the trend of the curve of breakthrough volume versus flow rate, the dissolution pattern, and its corresponding flow rate intervals, but changes the specific values of breakthrough volumes and the morphological details of dissolution patterns. As the flow rate increases, this effect becomes greater. Compared with the zone of a lower degree of dolomitization, the zone of a higher degree of dolomitization always hinders the acid-rock reaction. The hindering capacity cannot be ignored when the calcite content varies along the flow direction and is negligible when it varies perpendicular to the flow direction. This is not evident in reservoirs with low dolomitization. The breakthrough volume under linear mineral distribution is close to that under uniform mineral distribution. The stepwise mineral distribution limits the acid-rock reaction and increases the breakthrough volume. As the number of steps increases, the results are closer to those of the linear mineral distribution.