Anaerobic digestion (AD) is a crucial bioenergy source widely applied in wastewater treatment. However, its efficiency improvement is hindered by complex microbial communities and sensitivity to feedstock properties. We, thus, propose a hybrid quantum-classical machine learning (Q-CML) regression algorithm using a quantum circuit learning (QCL) strategy. Combining a variational quantum circuit with a classical optimiser, this approach predicts biogas production from operational data of 18 full-scale mesophilic AD sites in the UK. Tailored for noisy intermediate-scale quantum (NISQ) devices, the low-depth QCL model outperforms conventional regression methods (R²: 0.53) and matches the performance of a classical multi-layer perceptron (MLP) regressor (R²: 0.959) with significantly fewer parameters and better scalability. Comparative analysis highlights the advantages of quantum superposition and entanglement in capturing intricate correlations in AD data. This study positions Q-CML as a cutting-edge solution for optimising AD processes, boosting energy recovery, and driving the circular economy.