Neural circuits continuously integrate noisy sensory stimuli with predictions that often do not perfectly match, requiring the brain to combine these conflicting feedforward and feedback inputs according to their uncertainties. However, how the brain tracks both stimulus and prediction uncertainty remains unclear. Here, we show that a hierarchical prediction-error network can estimate both the sensory and prediction uncertainty with positive and negative prediction-error neurons. Consistent with prior hypotheses, we demonstrate that neural circuits rely more on predictions when sensory inputs are noisy and the environment is stable. By perturbing inhibitory interneurons within the prediction-error circuit, we reveal their role in uncertainty estimation and input weighting. Finally, we link our model to biased perception, showing how stimulus and prediction uncertainty contribute to the contraction bias.