To enhance and highlight the authentication and traceability of table olive oil, we considered the analysis of 11 Tunisian table olive cultivars based on seven SNP molecular markers (SOD, CALC, FAD2.1, FAD2.3, PAL70, ANTHO3, and SAD.1) localized in six different genes. Accordingly, we assessed the potential genotype-phenotypes links between the seven SNPs, on the one hand, and the quantitative and qualitative parameters, on the other. The obtained genotypes were analyzed with computational biology tools based on bivariate analysis, multinomial logistic regression, and the Bayesian networks modeling. Obtained results showed that PAL70 SNP marker was negatively influenced by the phenol rate (r = -0.886; p <0.001), the oxidative stability (r = -0.884; p <0.001), traducing a direct effect of the PAL70 genotype deviations on the proportion of total phenol for each variety. Additionally, we revealed a significant association of SAD.1 marker with the content of the linolenic unsaturated fatty acids (C18:3; p=0.046). Moreover, SAD.1 was positively correlated with the saturated stearic acid C18:0 (r = 0.644; p = 0.032) based on multinomial logistic regression and Bayesian networks modeling, respectively. This research work provides better understanding and characterization of the quality of Tunisian table olive and supplies a significant knowledge and data information for table olive traceability and breeding.