Disclosed is a drying system of a laundry washing machine, the system comprising an air duct and a filter device arranged in the air duct. The filter device comprises a filter screen and a cleaning portion, and the cleaning portion comprises a mounting plate and a water inlet pipe, wherein the filter screen is mounted on the mounting plate, and the water inlet pipe extends in the direction of the filter screen. One side of the mounting plate is connected to the water inlet pipe, and an inner cavity of the mounting plate is in communication with an inner cavity of the water inlet pipe so as to form a cleaning channel. An inlet end of the cleaning channel is located at the end, away from the mounting plate, of the water inlet pipe, and an outlet end of the cleaning channel is located on one side of the filter screen. Further disclosed is a washing machine.