Continuous polymerization apparatus including a first reactor of a complete mixing type and a second reactor of a complete mixing type (10, 20). Each of the reactors (10, 20) is provided with a supply port (11a, 21a), an effluent port (11b, 21b), and a temperature detecting means (T) for detecting a temperature in the reactor, wherein the supply port (11a) of the first reactor (10) is connected to the supply sources (1, 3) of a raw material monomer and a polymerization initiator, and the effluent port (11b) of the first reactor is connected through a connection line (15) to the supply port (21a) of the second reactor (20). Connection line (15) is combined with a secondary line (15′) for supplying a raw material monomer at a combining part (M) located between the effluent port (11b) of the first reactor (10) and the supply port (21a) of the second reactor (20).