Studies were conducted to determine the effects of supplementation upon intake, growth and carcass traits of Ovin Martinik hair sheep. Forty lambs weighing 20 ± 3.7 kg live weight (LW) were reared after weaning in individual pens during a 4-month experimental study. Four supplement levels were compared (10 lambs per treatment): the L0 group received the basal diet (tropical forage 0.75 UFL and 73 PDIN g kg−1 DM, INRA system) without concentrate, the L150, L300 and L600 groups were offered in addition 150, 300 and 600 g day−1 of concentrate (1.15 UFL and 151 PDIN g kg−1 DM), respectively. Intake (5 days a week) and growth patterns (every fortnight) were measured on the 40 lambs, while digestibility measurements (five times throughout the experimental period) were determined on half of the animals fitted with faecal bags and which were slaughtered according to the standard procedure at 33–35 kg live weight for assessment of carcass traits and meat quality. The total dry matter intake (DMI) and digestibility increased (P < 0.01) with the inclusion ratio of the concentrate in the diet: 82 g DM kg W−0.75 vs. 97 g DM kg W−0.75 and 65% vs. 73% between the two extreme groups, whereas forage DMI decreased and the forage substitution ratio was calculated to be 0.65. Growth and feed/gain ratios significantly (P < 0.01) improved among the groups L0, L150 and L300, from an average of 134–188 g day−1 and 7.0–5.7, respectively. The differences observed between L300 and L600 were not significant. Carcass weight and dressing out percentages significantly (P < 0.01) increased with the addition of concentrate to the ration: from 13.1 to 15.6 kg and from 39 to 46%, from L0 to L600, respectively. Consequently, the weights of the different cuts of the carcass varied. There was a significant effect of the supplementation level on the accumulation of internal fat tissues: the kidney fat weight increased from 107 to 237 g from the L0 to the L600 groups. No significant effect was observed on the carcass quality scores, the ultimate pH and the colour parameters of the meat. By increasing the nutritional density of the diet, it was possible to obtain well-conformed and heavier carcasses, with no apparent detrimental effect on the quality. The optimal supplement supply with good quality grass would be 300 g day−1 in our conditions.