A vehicle-mounted software updating apparatus for performing a software update by downloading software from outside a vehicle, the vehicle-mounted software updating apparatus comprising: a storage unit configured to store a past on/off status of an accessory; a software update period determining unit configured to estimate an optimum period having a high probability of the accessory being off based on information stored in the storage unit; and a software update performing unit configured to perform the software update in the software update period determined by the software update period determining unit, wherein the software update period determining unit is configured to estimate an optimum period among a plurality of periods within 24 hours, the optimum period having a high probability of the accessory being off, wherein each of the plurality of periods is defined by a change in an on/off state of the accessory based on information of a predetermined number of days in the past that is stored in the storage unit, and determine the software update period based on the estimated period, characterized in that the software update period determining unit is further configured to determine whether the estimated optimum period is longer than a required download time necessary for a software update, and determine a software update period within the estimated optimum period when it is determined that the estimated optimum period is longer than the required download time necessary for the software update, allocate a first weight, a second weight, and a third weight to a period in which the accessory was on continuously for a predetermined time or more, a period in which the accessory was on continuously for less than the predetermined time, and a period in which the accessory was not on, respectively, the first weight having a higher value than the second weight and the second weight having a higher value than the third weight, calculate a total of the weights of the predetermined number of days for each of the periods in the 24 hours, and determine the optimum period with the highest probability of the accessory being off by comparing the total weights among the periods, wherein the period having the minimum total weight among the periods is determined to be optimum period with the highest probability of the accessory being off. a storage unit configured to store a past on/off status of an accessory; a software update period determining unit configured to estimate an optimum period having a high probability of the accessory being off based on information stored in the storage unit; and a software update performing unit configured to perform the software update in the software update period determined by the software update period determining unit, wherein the software update period determining unit is configured to estimate an optimum period among a plurality of periods within 24 hours, the optimum period having a high probability of the accessory being off, wherein each of the plurality of periods is defined by a change in an on/off state of the accessory based on information of a predetermined number of days in the past that is stored in the storage unit, and determine the software update period based on the estimated period, characterized in that the software update period determining unit is further configured to determine whether the estimated optimum period is longer than a required download time necessary for a software update, and determine a software update period within the estimated optimum period when it is determined that the estimated optimum period is longer than the required download time necessary for the software update, allocate a first weight, a second weight, and a third weight to a period in which the accessory was on continuously for a predetermined time or more, a period in which the accessory was on continuously for less than the predetermined time, and a period in which the accessory was not on, respectively, the first weight having a higher value than the second weight and the second weight having a higher value than the third weight, calculate a total of the weights of the predetermined number of days for each of the periods in the 24 hours, and determine the optimum period with the highest probability of the accessory being off by comparing the total weights among the periods, wherein the period having the minimum total weight among the periods is determined to be optimum period with the highest probability of the accessory being off.