A network management apparatus includes: a determination part that determines, when a set of transmission rates set for a plurality of groups including one or more flows is gradually changed from a start state to an end state, a set(s) of transmission rates used in an intermediate state(s) in such a manner that a constraint(s) on a bandwidth(s) of a link(s) through which a flow(s) passes is satisfied; and a setting part that gradually changes the set of transmission rates set for the plurality of groups from the start state to the end state while using the determined set(s) of transmission rates in the intermediate state(s).