Adaptive control is an effective approach for mitigating undesirable deviations in prescribed closed-loop plant behavior. However, conventional adaptive control methods often exhibit slow responses in various control tasks. This paper introduces a novel adaptive control method to achieve fixed-time synchronization in a class of coupled neural networks. We present coupled neural networks with multiple switching topologies and design a fixed-time adaptive control strategy for this system. Furthermore, we establish a criterion to ensure the fixed-time stability of the closed-loop system. Two numerical examples are provided to demonstrate the effectiveness and accuracy of the theoretical results.