A method for discovery and change of a PMTU between a source node and a destination node on a dynamic IP network comprises generating a PMTU discovery packet having a MTU information storage space in which an MTU value on a routing path between the source node and the destination node is stored; transmitting the generated PMTU discovery packet to the destination node; and if a response packet to the PMTU discovery packet from the destination node is received, changing the PMTU according to MTU information contained in the response packet, wherein the MTU value stored in the MTU information storage space is compared with a link MTU value on a path which the PMTU discovery packet traverses, and the smaller one of the stored MTU value and the link MTU value on the path which the packet traverses is stored in the MTU information storage space.