The experiment was conducted at Alamata Agricultural Research Center, Ethiopia using 20 Afar rams with an initial body weight (BW) of 18.2 +/- 1.76 (mean +/- SD) kg. The objectives were to study the effect of supplementation with concentrate mix consisting of wheat bran (WB), noug seed cake (NSC) and sesame seed cake (SSC) at the ratio of 2:1:1 on dry matter (DM) basis, respectively on feed intake, digestibility, BW gain and carcass parameters of Afar rams fed tef (Eragrostis tef) straw basal diet. The experiment was arranged with four treatments and five replications in a randomized complete block design. The treatments included feeding sole tef straw (T1, control), and daily supplementation with the concentrate mix offered at 150 (T2, low), 250 (T3, medium) and 350 (T4, high) g DM per head. Total DM intake, crude protein (CP) digestibility, daily BW gain (P < 0.001), DM and organic matter (OM) digestibility, and carcass parameters (P < 0.05) were higher in the supplemented than in the control treatment. Intake of tef straw reduced as the level of supplementation increased, whereas the contrary was true for CP intake. Performance in carcass parameters was better for the medium compared to the low level of concentrate mix supplementation. Moreover, the medium level of supplementation did not substitute tef straw intake. Therefore, it is concluded that the medium level of concentrate mix supplement maintained the utilization of the roughage feed and resulted in better carcass parameters.