Hypertension is a major risk factor for cardiovascular disease, coronary heart disease, stroke, and other diseases. According to statistics from the World Health Organization, the number of deaths caused by cardiovascular disease is as high as 17 million each year. In this study, a convolutional fuzzy neural predictor (CFNP) model was developed to estimate systolic blood pressure (SBP), diastolic blood pressure (DBP), and mean arterial pressure (MAP). The developed CFNP model uses a convolutional layer to extract features from photoplethysmography and electrocardiography sensing signals. It then uses a maximum pooling layer to compress these features to reduce the number of calculations. A feature fusion layer is added to the developed model to integrate information from the convolutional layer and reduce the input dimension of the fuzzy neural network (FNN). Finally, the fused feature information is sent to the FNN for prediction. The Shapley additive explanations (SHAP) method was used in this study to perform feature analysis and calculate the contribution of each extracted feature. On the basis of the aforementioned analysis and calculations, superior feature sets were selected for the developed model. Experimental results indicated that the mean absolute errors (MAEs) of the CFNP model in predicting MAP, SBP, and DBP when using the superior feature sets obtained through SHAP analysis were 9.34, 14.13, and 9.39 mmHg, respectively. The proposed model also outperformed other machine learning models in terms of MAE in MAP, SBP, and DBP predictions.