This paper addresses the finite-time stability problem for a class of fractional-order Cohen–Grossberg neural networks characterized by fuzzy logic operators and time-varying delays. The coexistence of variable delays and fuzzy feedback structures poses considerable challenges in deriving effective stability conditions. To tackle these difficulties, a delay-dependent estimation strategy based on a weighted envelope framework is developed to characterize the influence of delayed states. Subsequently, a novel fractional Gronwall-type inequality is established and utilized to derive a sufficient finite-time stability criterion for the investigated neural network model. The obtained criterion explicitly captures the effects of fuzzy min/max operations and time-varying delays. Finally, three simulation examples are provided to verify the applicability and effectiveness of the proposed theoretical results.