It is well known in Traditional Chinese Medicine (TCM) that a person's wrist pulse signal can reflect their health condition. Recently, many computerized wrist pulse AI systems have been proposed to simulate a practitioner's three fingers in order to acquire the wrist pulse signals (three positions/channels) from a candidate's wrist dynamically, before evaluating their health status based on the various feature extraction and detection methods. However, few works have investigated the correlation of the extracted features from the three wrist channels and comprehensively fused the various features together, which can improve the performance of wrist pulse diagnosis. In this paper, we propose a graph based multichannel feature fusion (GBMFF) method to utilize the multichannel features of the wrist pulse signals effectively. In detail, two different sensors, i.e., pressure and photoelectricity are used to capture the three channels of the wrist pulse signals. These are used to generate two different features by applying the stacked sparse autoencoder and wavelet scattering. Each feature of one wrist pulse sample is regarded as a node associated with its corresponding feature vector, and used to construct a graph for one candidate. A novel algorithm is implemented to construct different graphs for different candidates, which are used for wrist pulse diagnosis by developing graph convolutional networks. Experimental results indicate that our proposed AI-based method can obtain superior performances compared to other state-of-the-art approaches.