Major depressive disorder (MDD) is frequently accompanied by the symptoms of clinical anxiety. Since our previous research has found that n-3 PUFA supplementation alleviates anxiety in MDD, this study was aimed to further explore whether n-3 PUFA supplementation improves anxiety symptoms in depression by directly manipulating fatty acid levels. A secondary analysis of biomarker data (erythrocyte fatty acid composition) collected as part of the randomized clinical trial which investigated the adjunctive effect of n-3 PUFAs was conducted on 72 venlafaxine-treated outpatients with first-diagnosed, drug-naïve depression. All participants with longitudinal biomarker data were included in the association analysis to determine how n-3 PUFA supplementation influences fatty acid composition and alleviates anxiety symptoms in depression. Decreases of the C20:3n6 were found in all participants at both follow-up time points (χ2 = 96.36, p = 0.000). The n-3 index (χ2 = 10.59, p = 0.001), EPA (χ2 = 24.31, p = 0.000), and C22:5n3/C20:5n3 ratio (χ2 = 10.71, p = 0.001) were increased, while C22:4n6 (χ2 = 7.703, p = 0.006) was decreased in n-3 PUFA group compared to the placebo group. The improvement in anxiety symptoms positively correlates with the extent of reduction of C16:0, C18:0, and total fatty acid levels as well as D5 desaturase activity (p < 0.05). These data suggest that the anxiolytic effect exerted by n-3 PUFAs in first-diagnosed, drug-naïve depression is manipulated by erythrocyte fatty acid levels. Saturated fatty acid levels have an important role in predicting the severity of anxiety symptoms.