Catalyzes the post-translational formation of 4-hydroxyproline. Probably hydroxylates skp1 on Pro-143. 2-oxoglutarate + L-prolyl-[Skp1 protein] + O2 = CO2 + succinate + trans-4-hydroxy-L-prolyl-[Skp1 protein] Binds 1 Fe(2+) ion per subunit. Inhibited by the prolyl-hydroxylase inhibitors alpha,alpha'-dipyridyl and ethyl 3,4-dihydroxybenzoate. Heterotetramer of two alpha-1 chains and two beta chains (the beta chain is the multi-functional PDI). Belongs to the P4HA family.