This paper investigates new feature extraction and regression methods for predicting cuffless blood pressure from PPG signals. Cuffless blood pressure is a technology that measures blood pressure without needing a cuff. This technology can be used in various medical applications, including home health monitoring, clinical uses, and portable devices. The new feature extraction method involves extracting meaningful features (time and chaotic features) from the PPG signals in the prediction of systolic blood pressure (SBP) and diastolic blood pressure (DBP) values. These extracted features are then used as inputs to regression models, which are used to predict cuffless blood pressure. The regression model performances were evaluated using root mean squared error (RMSE), R2, mean square error (MSE), and the mean absolute error (MAE). The obtained RMSE was 4.277 for systolic blood pressure (SBP) values using the Matérn 5/2 Gaussian process regression model. The obtained RMSE was 2.303 for diastolic blood pressure (DBP) values using the rational quadratic Gaussian process regression model. The results of this study have shown that the proposed feature extraction and regression models can predict cuffless blood pressure with reasonable accuracy. This study provides a novel approach for predicting cuffless blood pressure and can be used to develop more accurate models in the future.