Recent studies have raised concerns regarding racial and gender disparity in facial attribute classification performance. As these attributes are directly and indirectly correlated with the sensitive attribute in a complex manner, simple disparate treatment is ineffective in reducing performance disparity. This paper focuses on achieving counterfactual fairness for facial attribute classification. Each labeled input image is used to generate two synthetic replicas: one under factual assumptions about the sensitive attribute and one under counterfactual. The proposed causal graph-based attribute translation generates realistic counterfactual images that consider the complicated causal relationship among the attributes with an encoder-decoder framework. A causal graph represents complex relationships among the attributes and is used to sample factual and counterfactual facial attributes of the given face image. The encoder-decoder architecture translates the given facial image to have sampled factual or counterfactual attributes while preserving its identity. The attribute classifier is trained for fair prediction with counterfactual regularization between factual and corresponding counterfactual translated images. Extensive experimental results on the CelebA dataset demonstrate the effectiveness and interpretability of the proposed learning method for classifying multiple face attributes.