A vehicle state monitoring server configured to monitor a state of a battery mounted in a hybrid or electric vehicle provided with an electric motor as a prime mover, wherein the battery is configured to supply the electric power to the electric motor and to accumulate the regenerative power regenerated by the electric motor and wherein the battery can be charged by driving of the vehicle and by electric power supplied from an external power source, comprising: a database configured to store a vehicular identifier, as a number, a character or mark or a combination thereof intrinsic to an individual vehicle, for identifying the vehicle associated with a contact address of a user of the vehicle in a communication network, wherein the contact address comprising a mail address privately used by a user, a telephone number of a telephone machine owned by the user; a first monitoring-processing element configured to recognize a vehicle information capable of identifying the vehicular identifier of the vehicle and a last driving stopped duration of the vehicle according to communications with the communication network; wherein the vehicle state monitoring server is characterised by further comprising a second monitoring-processing element configured to send a message to the contact address stored in association with the vehicular identifier of the vehicle by the database on condition that the last driving stopped duration of the vehicle is equal to or longer than a reference duration, which is a factor for determining a timing for sending a message prompting necessary actions for charging the battery, namely prompting the driving of the vehicle, on the basis of the vehicle information recognized by the first monitoring-processing element, wherein the reference duration at a current time is set shorter as an elapsed time from an end time of the last driving duration of the vehicle becomes longer and under the consideration that the inclination angle of a downward slope and the travel distance contained in a travel route of the vehicle during the last driving duration are identified from the vehicle information and the difference of a decrement degree of the remaining amount of the battery related to the inclination angle of a downstream slope and the travel distance contained in a travel route identified by vehicle information and map information which is stored in the database and from which the inclination angle and the distance of each link constituting the route are identified. a database configured to store a vehicular identifier, as a number, a character or mark or a combination thereof intrinsic to an individual vehicle, for identifying the vehicle associated with a contact address of a user of the vehicle in a communication network, wherein the contact address comprising a mail address privately used by a user, a telephone number of a telephone machine owned by the user; a first monitoring-processing element configured to recognize a vehicle information capable of identifying the vehicular identifier of the vehicle and a last driving stopped duration of the vehicle according to communications with the communication network; wherein the vehicle state monitoring server is characterised by further comprising a second monitoring-processing element configured to send a message to the contact address stored in association with the vehicular identifier of the vehicle by the database on condition that the last driving stopped duration of the vehicle is equal to or longer than a reference duration, which is a factor for determining a timing for sending a message prompting necessary actions for charging the battery, namely prompting the driving of the vehicle, on the basis of the vehicle information recognized by the first monitoring-processing element, wherein the reference duration at a current time is set shorter as an elapsed time from an end time of the last driving duration of the vehicle becomes longer and under the consideration that the inclination angle of a downward slope and the travel distance contained in a travel route of the vehicle during the last driving duration are identified from the vehicle information and the difference of a decrement degree of the remaining amount of the battery related to the inclination angle of a downstream slope and the travel distance contained in a travel route identified by vehicle information and map information which is stored in the database and from which the inclination angle and the distance of each link constituting the route are identified.