The effect of increasing levels of supplementation with potato by-products on sheep body weight gain was evaluated. It was used 120 Junín sheep (69 female and 51 male) in a 2 x 5 factorial arrangement (two sexes x 5 feeding types). One treatment was 8 h/day of grazing and other four with addition of 0, 200, 400 and 600 g of potato by-products over ammoniated corn crop residue basal diet on 4-h a day grazing system for 24 days. Body weight gain was higher in males (p<0.01) in which the response pattern to the increasing levels of potato by-products supplementation was quadratic (p<0.01), and the level of 570 g of potato by-products gave a biological and economic performance similar to the full (8-h a day) grazing system. Data suggested that the inclusion of 570 g of potato byproducts on ammoniated corn crop residues is a practical and economical feeding strategy for fattening male sheep on a 4-h a day restricted grazing regime during the dry season in the Peruvian highlands.