Any process in which a virus stops, prevents, or reduces the frequency, rate or extent of host PKR (protein kinase regulated by RNA) activity. Activation of PKR involves dsRNA binding followed by autophosphorylation. Phosphorylated PKR can then phosphorylate downstream targets such as the translation initiation factor eIF2 to inhibit protein synthesis. Viruses encode a number of mechanisms to inhibit the host antiviral response via PKR, including direct interaction with PKR, promoting degradation of PKR or altering the subcellular location of PKR.