The invention provides equipment and a method for testing relative permeability of rock cores. The equipment comprises a clamping unit, a carbon dioxide supply unit, a salt water supply unit and a measuring unit. A clamp of the clamping unit comprises a seal cavity, an inlet and an outlet. The carbon dioxide supply unit comprises a booster pump, a first storage tank and a second storage tank. The second storage tank is connected with the inlet. Gaseous carbon dioxide is heated by a heat insulation device, supercritical carbon dioxide is prepared in the second storage tank, and the supercritical carbon dioxide in the second storage tank is injected into the rock cores by a carbon dioxide injection pump. The salt water supply unit and the carbon dioxide supply unit are connected to the inlet in a parallel mode, and a salt water solution in a salt water container is injected into the rock cores by a salt water injection pump. The measuring unit comprises an inlet pressure meter, a gas-liquid separator, an outlet pressure meter, a gas flow meter and a measurer, the inlet pressure meter and the carbon dioxide supply unit are connected to the inlet in a parallel mode, the gas-liquid separator and the outlet pressure meter are connected to the outlet in a parallel mode, the gas flow meter is connected to the output end of the gas-liquid separator, and the measurer is used for measuring liquid mass. By the equipment, the relative permeability of two-phase fluids in the rock cores can be simulated and researched.