The invention discloses a device for zero-power equal-density variable-temperature migration of compressed air and an operation method. The device comprises a first liquid piston cylinder, a second liquid piston cylinder, a first liquid pool, a second liquid pool, a first air storage tank, a second air storage tank, an air piston cylinder, hydraulic control equipment, pistons, piston rods, liquidvalves, air valves and pipelines. The device has the dual functions of heating boosting and cooling depressurizing, the requirement for carrying out variable-temperature and variable-pressure treatment on the compressed air in certain occasions can be met by using one single device, and therefore the variable-temperature and variable-pressure functions of the compressed air can be truly achieved;when the pressure is adjusted by utilizing the heat and mass exchange, the high-pressure air storage tank and the low-pressure air tank are isolated, in the boosting or depressurizing process, air inthe high-pressure air storage tank cannot directly communicate with air in the low-pressure air storage tank, and therefore the air pressure of the high-pressure air storage tank and the low-pressureair storage tank can be ensured to be stable and unchanged when the pressure is adjusted; and the air-liquid equal-density migration in the piston cavities can be realized, the volume of the compressed air in the equal-density migration process can be kept unchanged, external work is generated, when the pistons move, the pistons only need to overcome the friction force to do work, and therefore the energy consumption can be reduced.