This paper introduces Topological Consistency Adaptation (TCA), a novel approach to Continual Test-time Adaptation (CTTA) that addresses the challenges of domain shifts and error accumulation in testing scenarios. TCA ensures the stability of inter-class relationships by enforcing a class topological consistency constraint, which minimizes the distortion of class centroids and preserves the topological structure during continuous adaptation. Additionally, we propose an intra-class compactness loss to maintain compactness within classes, indirectly supporting inter-class stability. To further enhance model adaptation, we introduce a batch imbalance topology weighting mechanism that accounts for class distribution imbalances within each batch, optimizing centroid distances and stabilizing the inter-class topology. Experiments show that our method demonstrates improvements in handling continuous domain shifts, ensuring stable feature distributions and boosting predictive performance.