A plant alarm apparatus has: plant data input means for periodically taking in plant data; a latest plant data value table for temporarily storing latest values of the plant data; plant data recording means for taking out the latest values of the data of the latest plant data value table and storing them in a plant history data table; alarm-triggering value alteration means for updating the points for detecting plant abnormality in an alarm-triggering value registration table in response to a request by an operator; alarm-triggering condition editing means for registering alarm-triggering conditions of points showing a foretoken of abnormality; deviation-from-limit-value determining means for reading the stored values of the alarm-triggering value registration table and the alarm-triggering condition table and comparing the limit values of the points for detecting abnormality; and alarm notification output means for outputting the outcome of the comparison.