Finding alternative refrigerants is of extreme importance to mitigate anthropogenic climate change. Among the next-generation refrigerants, hydrocarbons (HCs) are of technical interest because they are natural, efficient, have low global warming potential (GWP), and zero ozone depletion potential (ODP). However, their flammability impedes their widespread usage for fire-safety reasons. The present work investigated zeotropic mixtures of hydrocarbons with carbon dioxide (CO2) as refrigerants for a simple vapor-compression refrigeration cycle, since their flammability risks are lower than those of pure hydrocarbons. Refrigerants were selected utilizing various screening steps based on environmental effects (such as GWP, ODP, and toxicity), thermophysical properties (such as critical temperature, and boiling point), and mixture data availability. The thermodynamic analysis for these selected zeotropic mixtures was performed for a cycle with a constant temperature of energy (heat) transfer fluid in both the evaporator and the condenser/gas cooler. Subsequently, performance parameters like the coefficient of performance and volumetric refrigeration capacity were compared for each of these blends at different operating conditions, and thus, the most promising hydrocarbon mixtures with CO2 were identified. As a result, the following four hydrocarbons, individually blended with CO2, were favorable in performance: propylene, dimethyl ether, propane, and isobutane. Further analysis was performed to determine the non-dimensional exergy destruction by the various components of the cycle.