An air conditioning device for vehicle, comprising: a refrigeration cycle including a compressor for sucking, compressing and discharging a refrigerant, a condenser for condensing the high-temperature and high-pressure refrigerant discharged from the compressor, an expansion valve for decompressing the refrigerant condensed in the condenser and an evaporator for evaporating the refrigerant through heat exchange between the refrigerant reduced in pressure by the expansion valve and surrounding air; a fuel cut execution means for executing a fuel cut during the deceleration of a vehicle so as to cut supply of fuel to an engine of the vehicle while the vehicle is moving; characterized in that it comprises a control means for increasing, when a vehicle speed drops below a first permitted vehicle speed (Vst) during the deceleration of the vehicle, an operation rate of the compressor for a predetermined period so as to become more than an operation rate of the compressor before a vehicle speed drops below the first permitted vehicle speed (Vst), the first permitted vehicle speed (Vst) being higher than a fuel cut recovery vehicle speed (Vacrec) when an air conditioner is on, the first permitted vehicle speed (Vst) being lower than a deceleration fuel cut execution starting vehicle speed (Vcf) at which execution of a fuel cut is started, the compressor being actuated when the vehicle speed drops form the first permitted vehicle speed (Vst) to the fuel cut recovery vehicle speed (Vacrec) and the air conditioner is on, the predetermined period indicating a period between a time when the vehicle speed drops below the first permitted vehicle speed (Vst) and a time immediately before the vehicle speed drops below the fuel cut recovery speed (Vacrec), wherein the first permitted vehicle speed (Vst) is a value set based on the fuel cut recovery vehicle speed (Vacrec) when the air conditioner is on, a time required to ensure cooling power of the evaporator and a predetermined assumed deceleration. a refrigeration cycle including a compressor for sucking, compressing and discharging a refrigerant, a condenser for condensing the high-temperature and high-pressure refrigerant discharged from the compressor, an expansion valve for decompressing the refrigerant condensed in the condenser and an evaporator for evaporating the refrigerant through heat exchange between the refrigerant reduced in pressure by the expansion valve and surrounding air; a fuel cut execution means for executing a fuel cut during the deceleration of a vehicle so as to cut supply of fuel to an engine of the vehicle while the vehicle is moving; characterized in that it comprises a control means for increasing, when a vehicle speed drops below a first permitted vehicle speed (Vst) during the deceleration of the vehicle, an operation rate of the compressor for a predetermined period so as to become more than an operation rate of the compressor before a vehicle speed drops below the first permitted vehicle speed (Vst), the first permitted vehicle speed (Vst) being higher than a fuel cut recovery vehicle speed (Vacrec) when an air conditioner is on, the first permitted vehicle speed (Vst) being lower than a deceleration fuel cut execution starting vehicle speed (Vcf) at which execution of a fuel cut is started, the compressor being actuated when the vehicle speed drops form the first permitted vehicle speed (Vst) to the fuel cut recovery vehicle speed (Vacrec) and the air conditioner is on, the predetermined period indicating a period between a time when the vehicle speed drops below the first permitted vehicle speed (Vst) and a time immediately before the vehicle speed drops below the fuel cut recovery speed (Vacrec), wherein the first permitted vehicle speed (Vst) is a value set based on the fuel cut recovery vehicle speed (Vacrec) when the air conditioner is on, a time required to ensure cooling power of the evaporator and a predetermined assumed deceleration.