Hemolysis in the GYRO centrifugal blood pump, under development at the Baylor College of Medicine, Houston, TX, is numerically predicted using the newly proposed tensor-based blood-damage model, as well as a traditional model. Three typical operating conditions for the pump are simulated with a special-purpose finite element-based flow solver, and a novel approach for tracing the pathlines in discretely represented time-varying flow in a complex domain is presented, and 271 pathlines are traced through the pump. Hemolysis is computed along the pathlines, and the accumulated hemolysis at the outflow is converted into standard clinical units. The cumulative hemolysis at the outlet of the pump is weighted with the flow rate associated with the pathlines, and a temporal average is obtained by releasing the tracer particles at different time intervals. Numerical predictions are compared to experimental hemolysis studies performed according to the American Society for Testing and Materials standards at the Baylor College of Medicine. The tensor-based blood-damage model is found to match very well with the experimental results, whereas the traditional model overpredicts the hemolysis. The success of the tensor-based blood-damage model is attributed to its construction, which accounts for blood-specific physical properties and phenomena. Hemolysis values at the typical operating conditions of the pump are found to be within the clinically accepted range.