Rotary blood pumps are expected to be used as an implantable ventricular assist device (VAD). In the VAD system, flow rate is important for monitoring of the state of a recipient and for automatic control to maintain appropriate blood perfusion. To obtain flow rate of the pump without any sensors, we proposed a method of estimating flow rate with supplied power and rotational speed using a time series model. To evaluate the accuracy of the proposed estimation method from the aspect of long-term use, we implanted NEDO PI Gyro pumps in a calf and performed a chronic animal experiment. Flow rate, supplied power and rotational speed were measured until post operation day (POD) 63, and the estimated flow rate was compared with the measured one. We confirmed that waveforms of the measured flow rate was sufficiently similar to the measured one, and correlation between them was higher than 0.9 in all the datasets. On the other hand, the root mean square error increased after 15 days. This error was probably due to the change in physiological condition, the operating point of the pump, or mild intima formation.