Interest in the preservation of autochthonous breeds such as the Blanca Andaluza goat (meat breed), raised under grazing-based management, has recently increased among Spanish farmers. A study of the possibilities of transformation to organic production needs to analyze the quality of their products. The aim of this study was to evaluate the fatty acid (FA) composition of muscle and adipose tissues of Blanca Andaluza goat kids under organic and conventional grazing-based management system. Twenty-four twin kids (12 males, 12 females) were selected from each system. The FA profile was determined in the longissimus thoracis muscle, kidney and pelvic fat. The percentages of C17:0, C17:1, C20:1, C20:4 n-6, C22:2 and several n-3 FAs were higher in organic meat; C12:0, C18:1 trans-11, CLA and C20:5 n-3 were lower in organic meat. The fat depots from the conventional kids showed lower percentages of C12:0, C14:0, C15:0, C17:0, C17:1, C18:3 n-3 and atherogenicity index, and higher percentage of C18:0. In the pelvic fat, the conventional kids displayed lower percentages of C16:0, C18:2 n-6 cis, PUFA, n-3 and n-6 FAs, and greater percentages of C18:1 n-9 cis and MUFA. The conventional kids displayed a major n6:n3 ratio in the kidney fat. No gender differences were observed. Significant differences were found only in some FA percentages of muscle and adipose tissues of suckling kids raised in organic and conventional livestock production systems, and due to this reason conventional grazing-based management farms could easily be transformed into organic production.