A dump management apparatus having a memory; and a processor that executes a process including: selecting, in response to receiving a notification of an occurrence of a failure from a failure node of a parallel computer having a plurality of nodes, a plurality of nodes that are not scheduled to execute a job within at least a first time needed to perform dump processing of a memory of the failure node and have a memory capacity needed to perform the dump processing as dump-processing target nodes from among a plurality of nodes within a reference range near the failure node; selecting the dump-processing target nodes with a first priority according to which a plurality of adjacent nodes are preferentially selected as a candidate over a plurality of dispersing nodes from among candidates for the dump-processing target nodes; and causing the failure node to transfer a dump file inside the memory of the failure node to memories of the dump-processing target nodes.