A vibration-damping device comprising: a tubular first mounting member connected to one of a vibration-generating part and a vibration-receiving part, and a second mounting part connected to another one of the vibration-generating part and the vibration-receiving part; an elastic body which elastically connects the first mounting member and the second mounting member; and a partitioning member which partitions a fluid chamber inside the first mounting member, the fluid chamber being filled with fluid, into a primary fluid chamber on one side having the elastic body as one part of a wall face and an auxiliary fluid chamber on another side. the partitioning member comprising: a limiting passage which communicates between the primary fluid chamber and the auxiliary fluid chamber, and generates fluid column resonance with respect to input vibration, thereby damping and absorbing the vibrations; a switching device which switches the resonance frequency of the limiting passage; a connection path which connects the primary fluid chamber and the auxiliary fluid chamber; a fluid pressure introduction path which communicates with the connection path, introduces fluid pressure in the connection path to the switching device, and activates the switching device; and a thin-film which is provided in the connection path and shuts off the communication between the primary fluid chamber and the auxiliary fluid chamber via the connection path. a tubular first mounting member connected to one of a vibration-generating part and a vibration-receiving part, and a second mounting part connected to another one of the vibration-generating part and the vibration-receiving part; an elastic body which elastically connects the first mounting member and the second mounting member; and a partitioning member which partitions a fluid chamber inside the first mounting member, the fluid chamber being filled with fluid, into a primary fluid chamber on one side having the elastic body as one part of a wall face and an auxiliary fluid chamber on another side. the partitioning member comprising: a limiting passage which communicates between the primary fluid chamber and the auxiliary fluid chamber, and generates fluid column resonance with respect to input vibration, thereby damping and absorbing the vibrations; a switching device which switches the resonance frequency of the limiting passage; a connection path which connects the primary fluid chamber and the auxiliary fluid chamber; a fluid pressure introduction path which communicates with the connection path, introduces fluid pressure in the connection path to the switching device, and activates the switching device; and a thin-film which is provided in the connection path and shuts off the communication between the primary fluid chamber and the auxiliary fluid chamber via the connection path. a limiting passage which communicates between the primary fluid chamber and the auxiliary fluid chamber, and generates fluid column resonance with respect to input vibration, thereby damping and absorbing the vibrations; a switching device which switches the resonance frequency of the limiting passage; a connection path which connects the primary fluid chamber and the auxiliary fluid chamber; a fluid pressure introduction path which communicates with the connection path, introduces fluid pressure in the connection path to the switching device, and activates the switching device; and a thin-film which is provided in the connection path and shuts off the communication between the primary fluid chamber and the auxiliary fluid chamber via the connection path.