The complexity of pedestrian interaction is a challenge for pedestrian trajectory prediction， and the existing algorithms are difficult to capture meaningful interaction information between pedestrians， which cannot intuitively model the interaction between pedestrians. To address this problem， a multi-head soft attention graph convolutional network was proposed. Firstly， a Multi-head Soft ATTention （MS ATT） combined with involution network was used to extract sparse spatial adjacency matrix and sparse temporal adjacency matrix from spatial and temporal graph inputs respectively to generate sparse spatial directed graph and sparse temporal directed graph. Then， a Graph Convolutional Network （GCN） was used to learn interaction and motion trend features from sparse spatial and sparse temporal directed graphs. Finally， the learned trajectory features were input into a Temporal Convolutional Network （TCN） to predict double Gaussian distribution parameters， thereby generating the predicted pedestrian trajectories. Experiments on Eidgenossische Technische Hochschule （ETH） and University of CYprus （UCY） datasets show that， compared with Space-time sOcial relationship pooling pedestrian trajectory Prediction Model （SOPM）， the proposed algorithm reduces the Average Displacement Error （ADE） by 2.78%， and compared to Sparse Graph Convolution Network （SGCN）， the proposed algorithm reduces the Final Displacement Error （FDE） by 16.92%.