Left ventricular assist device (LVAD) has been considered as a treatment option for end-stage congestive heart failure to assist an ailing heart to meet the circulatory demand. However, several important issues still challenge the long-term use of the LVAD as a bridge to transplantation or as a destination therapy. Specifically, the development of appropriate feedback controllers to adjust pump speed is crucial. The controller should automatically adjust the pump speed to meet different demands of blood without inducing suction. Suction means that the LVAD seeks to pump out more blood than that is available in the heart, which can collapse the failing heart and result in sudden death. In addition, hemodynamics involves variability due to patients' heterogeneity and stochastic nature of cardiovascular system. The variability poses significant challenges for the control system design of an LVAD. A self-tuning controller is developed in this work, which can adjust the pump speed to meet the physiological demands for different levels of activity, while accounting for variations in hemodynamics. A stochastic state space model will be firstly developed using a generalized polynomial chaos (gPC) expansion, which describes interactions between the LVAD and the cardiovascular system. In addition, the model can further predict the variability in pump flow for a finite future control horizon based on the current available information of pump flow. The prediction of variance is used as a tuning criterion to update the controller gain in a real time manner. The efficiency of the self-tuning control algorithm in this work is validated with two different case scenarios, representing different levels of activity for heart failure patients. The results show that the controller can successfully adjust the pump speed while avoiding suction.