A gas appliance monitoring system comprising: a center device, a gas meter including a flow rate measurer, a storage, and a meter communication unit, the flow rate measurer measuring a flow rate of gas in time series, the storage storing as flow rate data, the flow rate measured by the flow rate measurer, the meter communication unit performing communication with the center device; and the center device including a center communication unit, a data accumulation storage, and an analyzer, the center communication unit being configured to perform communication with the gas meter to receive the flow rate data, the data accumulation storage being configured to accumulate the flow rate data that has been received, and the analyzer being configured to analyze the flow rate data, wherein the center device includes a message distributor, and the center device is configured to monitor a state ofuse of the gas appliance (14, 15, 16) based on the flow rate data that has been accumulated in the data accumulation storage, wherein the gas meter is configured to detect a start of operation of a gas appliance (14, 15, 16), characterized in that, the gas meter is configured to store the flow rate data during predetermined periods (Tp, Tf) before and after the start of operation, and the gas meter is configured to transmit, from among pieces of the flow rate data that have been stored in the storage, only pieces of the flow rate data that correspond to the predetermined periods (Tp, Tf) before and after the start of operation, based on a request from the center device, so as to reduce an amount of data to be communicated, and the center device is configured to analyze the flow rate data that correspond to the predetermined periods (Tp, Tf) before and after the start of operation that has been accumulated in the data accumulation storage, by using the analyzer, and to generate a predetermined message based on analysis performed by the analyzer of the flow rate data that correspond to the predetermined periods (Tp, Tf) before and after the start of operation and distribute the predetermined message to a terminal of a user of the gas appliance (14, 15, 16), by using the message distributor. a center device, a gas meter including a flow rate measurer, a storage, and a meter communication unit, the flow rate measurer measuring a flow rate of gas in time series, the storage storing as flow rate data, the flow rate measured by the flow rate measurer, the meter communication unit performing communication with the center device; and the center device including a center communication unit, a data accumulation storage, and an analyzer, the center communication unit being configured to perform communication with the gas meter to receive the flow rate data, the data accumulation storage being configured to accumulate the flow rate data that has been received, and the analyzer being configured to analyze the flow rate data, wherein the center device includes a message distributor, and the center device is configured to monitor a state ofuse of the gas appliance (14, 15, 16) based on the flow rate data that has been accumulated in the data accumulation storage, wherein the gas meter is configured to detect a start of operation of a gas appliance (14, 15, 16), characterized in that, the gas meter is configured to store the flow rate data during predetermined periods (Tp, Tf) before and after the start of operation, and the gas meter is configured to transmit, from among pieces of the flow rate data that have been stored in the storage, only pieces of the flow rate data that correspond to the predetermined periods (Tp, Tf) before and after the start of operation, based on a request from the center device, so as to reduce an amount of data to be communicated, and the center device is configured to analyze the flow rate data that correspond to the predetermined periods (Tp, Tf) before and after the start of operation that has been accumulated in the data accumulation storage, by using the analyzer, and to generate a predetermined message based on analysis performed by the analyzer of the flow rate data that correspond to the predetermined periods (Tp, Tf) before and after the start of operation and distribute the predetermined message to a terminal of a user of the gas appliance (14, 15, 16), by using the message distributor.