Pricing gasoline and optimal allocation of resources have always been topics of interest for governments and experts. The increasing jump in the exchange rate has created a significant difference between the nominal and real prices of gasoline. Therefore, in the present study, a solution is proposed to narrow the existing gap by introducing a floating tax proportional to gasoline consumption, and its effect on household income distribution is examined. On the other hand, the regressive feature is a weakness of the consumption tax system that leads to undesirable effects on income distribution by imposing a higher tax burden on vulnerable classes. Therefore, the proposed scenario in this study is similar to the current pricing system and is in the form of two-tiered rates (quota-based and non-quota-based rates). The quota-based section is exempt from taxes and is similar to the past procedure, while the non-quota-based gasoline price is calculated based on individuals' consumption, considering a 5% tax for each liter of consumption exceeding the monthly quota. If the consumption increases, instead of receiving more subsidies, the higher expenses will accompany the consumer. In this regard, by using an almost ideal demand system model, the effects of implementing the proposed scenario on inequality and income distribution among urban households were studied, and categorized into four gasoline consumption groups (less than 60 liters, 60 to 80 liters, 80 to 120 liters, and more than 120 liters) during the years 2017-2020, considering some demographic variables such as household size, gender, age, marital status, employment, education, and household head's ownership of housing. Price and income elasticities were extracted, and the compensatory variation (CV) index of changes was calculated. Assuming the implementation of the proposed scenario and the constancy of prices for all commodity groups except gasoline, the household expenditure data was simulated, and inequality was calculated using the Gini coefficient. The results show that if the above-mentioned scenario is implemented by the government, assuming the constancy of prices for other commodity groups, a relative improvement in the Gini coefficient is obtained, indicating a reduction in inequality.