Organic Rankine cycle (ORC) is one of the most promising technologies to recover energy from low temperature waste heat. The heat sources usually experience fluctuations in temperature and mass flow rate, which makes it difficult to obtain satisfactory control performances of ORC systems. In this paper, a single neuron adaptive multi-step predictive control scheme is developed for an ORC based waste heat recovery (WHR) system with non-Gaussian disturbances. Since the non-Gaussian disturbances existed in WHR system follow heavy-tailed distribution, generalized correntropy is adopted as the performance index to characterize the system uncertainties. The weights of the single neuron controller are updated by optimizing the performance function. The whole implementation procedures of the proposed control strategy for the WHR are presented. As a contrast, the performances of the minimum error entropy (MEE) based controller and the mean square error (MSE) based controller are also tested. The proposed control scheme is confirmed to be more effective through simulations.