The aim of this study was to investigate the possibility of improving the composition of goat meat, in terms of the fatty acid composition of the different fat deposits. For this purpose, we used two groups of 12 female goats each of which had recently undergone a double birth. The animals were maintained under semi-extensive conditions and trough-fed with a concentrate that was either non-supplemented or supplemented with 50 g/kg of polyunsaturated fatty acids (PUFA)-rich fat protected against ruminant metabolism. The kid goats born to each group were suckled by their dams and a representative sample of each was slaughtered at 45 days after birth. The milk produced by the dams receiving the fat-supplemented diet contained fat with a lower content of saturated fatty acids and a higher content of n-3 PUFA, trans-C18: 1 and CLA. The kid goats suckled by these dams grew faster and the legs of the carcasses presented greater muscular development compared with the non-fat-supplemented diet group. The cover, intermuscular and intramuscular fat presented a different fatty acid composition, with a higher proportion of n-3 PUFA, trans C18: 1 and CLA, while that of n-6 PUFA remained unchanged. The change in the lipid metabolism of the kid goats was made evident by the blood levels of certain biochemical parameters. We discuss the improvement in the quality of the meat obtained, taking into account the feeding strategy provided and the class of animal in question.