The present invention discloses a rendezvous point convergence method and apparatus and relates to the field of communications, to solve a problem that an entire network cannot work normally for a long time because a network device cannot send a candidate RP advertisement message to a bootstrap router BSR when the network device served as a rendezvous point RP is entirely faulty. In the present invention, when a route of an original working RP is unreachable, a first node receives a bootstrap message sent by a BSR, where Holdtime of the original working RP carried in the bootstrap message is 0; and the first node disables the original working RP and enables a candidate RP as a new working RP according to the bootstrap message. The present invention is applicable to the field of communications to implement rendezvous point convergence.