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Negative and positive emotions are the risk and protective factors for the cause and prognosis of hypertension. This study aimed to use five photoplethysmography (PPG) waveform indices and affective computing (AC) to discriminate the emotional states in patients with hypertension. Forty-three patients with essential hypertension were measured for blood pressure and PPG signals under baseline and four emotional conditions (neutral, anger, happiness, and sadness), and the PPG signals were transformed into the mean standard deviation of five PPG waveform indices. A support vector machine was used as a classifier. The performance of the classifier was verified by using resubstitution and six-fold cross-validation (CV) methods. Feature selectors, including full search and genetic algorithm (GA), were used to select effective feature combinations. Traditional statistical analyses only differentiated between the emotional states and baseline, whereas AC achieved 100% accuracy in distinguishing between the emotional states and baseline by using the resubstitution method. AC showed high accuracy rates when used with 10 waveform features in distinguishing the records into two, three, and four classes by applying a six-fold CV. The GA feature selector further boosted the accuracy to 78.97%, 74.22%, and 67.35% in two-, three-, and four-class differentiation, respectively. The proposed AC achieved high accuracy in categorizing PPG records into distinct emotional states with features extracted from only five waveform indices. The results demonstrated the effectiveness of the five indices and the proposed AC in patients with hypertension.