Interest in the preservation of autochthonous breeds such as the Payoya goat (dairy breed), raised using extensive or semi-extensive grazing, has also recently increased among Spanish farmers. A study of the possibilities of transformation to organic production needs to analyze the quality of their products, specially the suckled kids. The objective of this study was to evaluate the fatty acid (FA) composition of Payoya goat kids under organic and conventional grazing–based management system. Forty-eight goat kids were selected (12 males and 12 females from each management system). The FA profile was determined in the Longissimus thoracis muscle, kidney and pelvic fat. Few gender differences were observed in the muscle and in the fat depots. The ratios of C14:0, C18:1 trans-11-(VA), and several n-3 FA were higher in organic kid meat than in conventionally reared kid meat. Conventional kid fat depots have presented higher percentage of conjugated linoleic acid (CLA), lower CLA desaturase index, lower percentage of n-3 polyunsaturated fatty-acid (PUFA) and, consequently, higher n6:n3 PUFA ratio than organic kids. In conclusion, 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, probably due because the dams, in both experimental farms, were raised with similar semi-extensive system based on the grazing of natural pastures. Due to this reason, conventional grazing–based management farms could easily be transformed into organic production facilities.