A naturally occurring or recombinant urate oxidase (uricase) covalently coupled to poly(ethylene glycol) or poly(ethylene oxide) (both referred to as PEG), wherein an average of 2 to 10 strands of PEG are conjugated to each uricase subunit and the PEG has an average molecular weight between about 5 kDa and 100 kDa. The resulting PEG-uricase conjugates are substantially non-immunogenic and retain at least 75% of the uricolytic activity of the unmodified enzyme.