The experiment consisting of 7 days of digestibility and 90 days of feeding trial was conducted at Wogda (Ethiopia) to determine the effect of supplementation of graded levels of concentrate mix (CM) on feed intake, digestibility, and body weight (BW) change in hay-based feeding of Simada sheep. Twenty-yearling Simada sheep with a mean initial BW of 17.9 +/- 0.81 kg (mean +/- SD) were used in randomized complete block design arranged into five blocks of four animals. The four dietary treatments that consisted of hay alone (T1), hay +150 g dry matter (DM; T2, low), hay +250 g DM (T3, medium), and hay +350 g DM (T4, high) CM were randomly assigned to each sheep within a block. The CM consisted of wheat bran (WB), noug seed (Guizotia abyssinica) meal and safflower (Carthamus tinctorius) seed meal at the ratio of (2:1:1), respectively. Supplementation with T2 and T3 increased (P < 0.001) total DM and organic matter intake than the control treatment. Overall, supplementation improved (P < 0.001) crude protein intake, digestibility, feed conversion efficiency, BW gain, and profitability compared to the control, whereas sheep on the high than the low and medium level of supplementation performed better in these parameters among the supplemented treatments. From the results of this study, T4 is recommended as the best level of supplementation since it resulted in better nutrient utilization, animal performance, and profitability.