A continuous polymerization apparatus uses at least a first reactor and a second reactor (10, 20). Each of the reactors (10, 20) comprises a supply port (11a, 21a) and an effluent port (11b, 21b). The supply port (11a) of the first reactor (10) is connected to supply sources (1, 3) of a raw material monomer and a polymerization initiator, and the effluent port (11b) thereof is connected to the supply port (21a) of the second reactor (20) by a connection line (15a). The connection line (15a) is combined with a replenishing line (15b) through an injection valve (50) at a combining part. The injection valve (50) comprises, in a full closure state thereof, a clearance that may cause a fluid comprising at least the raw material monomer to flow from the replenishing line (15b) to the connection line (15a).