Double-stranded DNA viruses utilise machinery, made of terminase proteins, to package viral DNA into the capsid. For cos bacteriophage, a defined signal, recognised by small terminase, flanks each genome unit. Here we present the first structural data for a cos virus DNA packaging motor, assembled from the bacteriophage HK97 terminase proteins, procapsids encompassing the portal protein, and DNA containing a cos site. The cryo-EM structure is consistent with the packaging termination state adopted after DNA cleavage, with DNA density within the large terminase assembly ending abruptly at the portal protein entrance. Retention of the large terminase complex after cleavage of the short DNA substrate suggests that motor dissociation from the capsid requires headful pressure, in common with pac viruses. Interestingly, the clip domain of the 12-subunit portal protein does not adhere to C12 symmetry, indicating asymmetry induced by binding of the large terminase/DNA. The motor assembly is also highly asymmetric, showing a ring of 5 large terminase monomers, tilted against the portal. Variable degrees of extension between N- and C-terminal domains of individual subunits suggest a mechanism of DNA translocation driven by inter-domain contraction and relaxation.