Heart failure (HF) is a major global health concern and is increasing in prevalence. It affects the larynx and breathing - thereby the quality of speech. In this article, we propose an approach for the automatic detection of people with HF using the speech signal. The proposed method explores mel-frequency cepstral coefficient (MFCC) features, glottal features, and their combination to distinguish HF from healthy speech. The glottal features were extracted from the voice source signal estimated using glottal inverse filtering. Four machine learning algorithms, namely, support vector machine, Extra Tree, AdaBoost, and feed-forward neural network (FFNN), were trained separately for individual features and their combination. It was observed that the MFCC features yielded higher classification accuracies compared to glottal features. Furthermore, the complementary nature of glottal features was investigated by combining these features with the MFCC features. Our results show that the FFNN classifier trained using a reduced set of glottal + MFCC features achieved the best overall performance in both speaker-dependent and speaker-independent scenarios.