The invention provides a Fischer-Tropsch wax and catalyst filtering and back-flushing method for a Fischer-Tropsch synthetic slurry bed reactor. The method comprises the following steps of: 1, in production mode, opening a clear solution extracting system, and extracting Fischer-Tropsch wax to a crude wax product buffer tank with set pressure; 2, in the production mode, when the back-flushing time interval value reaches a set value, opening a back-flushing system to back-flushing a filter element; and 3, when the back-flushing time reaches a set value, closing the back-flushing system, and newly extracting the Fischer-Tropsch wax to the crude wax product buffer tank with the set pressure. By automatically controlling a filter system and the back-flushing system and automatically back-flushing the filter element according to the time period or the back-flushing operation pressure difference, the Fischer-Tropsch wax can be stably and effectively extracted from the reactor for a long period, and stable and continuous operation of the Fischer-Tropsch synthetic slurry bed reactor is realized.