The invention, which belongs to the technical field of establishment of an underground salt cavern gas storage, discloses a physical simulation apparatus and method of convection and diffusion of a salt-cavern gas storage cavity. The physical simulation apparatus comprises a simulation box, a displacement pump, a discharge pipe, a conductivity meter, a shooting device opposite to the simulation box, a cavity construction tubular column and a computer. The displacement pump and the discharge pipe are connected to the cavity construction tubular column; a first flowmeter is connected between the displacement pump and the simulation box; a second flowmeter is also arranged at the discharge pipe; and the shooting device, the first flowmeter, and the second flowmeter are connected to the computer by an operable way. According to the invention, simulation of various working conditions is carried out in the simulation box; fresh water is injected into the displacement pump and the discharge pipe discharges brine to make convection and diffusion phenomena, thereby reflecting the working condition and environment of the cavity construction process of the salt cavern gas storage actually. Therefore, the method and process parameters that are obtained based on the simulation apparatus and method and are used for accelerating a rock salt cavity construction speed become true and accurate, thereby improving the cavity construction speed and the cavity shape controlling beneficially.