Prediction techniques are extensively used in medical applications and health devices. The prediction of the infusion flow rate and its speed in a smart wireless infusion pump is necessary to provide precise drug flow. This paper has developed the prediction model to predict the lag time and infusion pump speed using the Gaussian process regression (GPR) technique with a squared exponential kernel. The present smart wireless infusion pump is usually incorporated with its smart drug library. The required parameters such as drug dosage, drug flow rate are utilized as inputs to predict the pump speed, minimize start-up delays using proposed regression techniques. The evaluation of prediction models is done by the coefficient of determination (R2), mean absolute error (MAE), and root-mean-squared error (RMSE). These prediction results are verified for predicting lag time and infusion pump speed for two different carrier flowrates, 10 ml/hr, 50 ml/hr. The study's outcome indicates that the regression model GPR has better prediction accuracy with a mean coefficient of determination of 0.99. Hence, the GPR technique can achieve quick infusion speed with minimized lag time,the optimal flow rate for smart infusion pumps.