A new suction detection algorithm for rotary Left Ventricular Assist Devices (LVAD) is presented. The algorithm is based on a Lagrangian Support Vector Machine (LSVM) model. Six suction indices are derived from the LVAD pump flow signal and form the inputs to the LSVM classifier. The LSVM classifier is trained and tested to classify pump flow patterns into three states: No Suction, Approaching Suction, and Suction. The proposed algorithm has been tested using existing in vivo data. When compared to three existing methods, the proposed algorithm produced superior performance in terms of classification accuracy, stability, and learning speed. The ability of the algorithm to detect suction provides a reliable platform in the development of a pump speed controller that has the capability of avoiding suction.