The natural phenomenon associated with the chemical dissolution of dissolvable minerals of rocks can be employed to develop innovative technology in mining and oil extracting engineering. This paper presents a new alternative approach for theoretically dealing with chemical dissolution front (CDF) propagation in fluid-saturated carbonate rocks. Note that the CDF is represented by the porosity front in this study. In this new approach, the porosity, pore-fluid velocity and acid concentration are directly used as independent variables. To illustrate how to use the present new approach, an acidization dissolution system (ADS) consisting of carbonate rocks, which belongs to one of the many general chemical dissolution systems (CDSs), is taken as an application example. When the acid dissolution capacity (ADC) number (that is defined as the ratio of the volume of the carbonate rock dissolved by an acid to that of the acid) approaches zero, the present new approach can be used to obtain analytical solutions for the stable ADS. However, if the ADC number is a nonzero finite number, then numerical solutions can be only obtained for the ADS, especially when the ADS is in an unstable state. The related theoretical results have demonstrated that: (1) When the ADS is in a stable state and in the case of the ADC number approaching zero, the present new approach is mathematically equivalent to the previous approach, in which the porosity, pore-fluid pressure and acid concentration are used as independent variables. However, when the ADS is in an unstable state, the use of the present new approach leads to a free parameter that needs to be determined by some other ways. (2) The existence of a non-step-type dissolution front within a transient region should at least satisfy that none of the ADC number, injected acid velocity and reciprocal of the dissolution reaction rate is equal to zero in the stable ADS.