Energy-efficient and noisy-adaptive signal processing system are in high demand of edge biomedical applications. In this paper, we present a Noise-Adaptive Memristive Bayesian Neural Network (NMBNN) architecture for various biosignal applications. The memristor has the inherent physical property of exhibiting variability in resistance, which makes it a promising candidate of uncertainty weight in Bayesian Neural Networks (BNN). The NMBNN architecture combines the noise-resilient attributes of BNN with the implementation of an energy-efficient RRAM array. By utilizing BNN’s probabilistic predictions and implementation with the conductance fluctuations of memristors, NMBNN offers a robust and energy-efficient solution adept at processing biosignals in noisy environments. In order to evaluate the network robustness, we conduct the experiments to introduce multiple types of noise as adversarial sample. The experimental results indicate that the proposed NMBNN approach has the advantages of being both noise-adaptive and energy-efficient.