Coronavirus disease 2019 (COVID-19) is rapidly spreading. Researchers around the world are dedicated to finding the treatment clues for COVID-19. Drug repositioning, as a rapid and cost-effective way for finding therapeutic options from available FDA-approved drugs, has been applied to drug discovery for COVID-19. In this study, we develop a novel drug repositioning method (VDA-KLMF) to prioritize possible anti-SARS-CoV-2 drugs integrating virus sequences, drug chemical structures, known Virus-Drug Associations, and Logistic Matrix Factorization with Kernel diffusion. First, Gaussian kernels of viruses and drugs are built based on known VDAs and nearest neighbors. Second, sequence similarity kernel of viruses and chemical structure similarity kernel of drugs are constructed based on biological features and an identity matrix. Third, Gaussian kernel and similarity kernel are diffused. Forth, a logistic matrix factorization model with kernel diffusion is proposed to identify potential anti-SARS-CoV-2 drugs. Finally, molecular dockings between the inferred antiviral drugs and the junction of SARS-CoV-2 spike protein-ACE2 interface are implemented to investigate the binding abilities between them. VDA-KLMF is compared with two state-of-the-art VDA prediction models (VDA-KATZ and VDA-RWR) and three classical association prediction methods (NGRHMDA, LRLSHMDA, and NRLMF) based on 5-fold cross validations on viruses, drugs, and VDAs on three datasets. It obtains the best recalls, AUCs, and AUPRs, significantly outperforming other five methods under the three different cross validations. We observe that four chemical agents coming together on any two datasets, that is, remdesivir, ribavirin, nitazoxanide, and emetine, may be the clues of treatment for COVID-19. The docking results suggest that the key residues K353 and G496 may affect the binding energies and dynamics between the inferred anti-SARS-CoV-2 chemical agents and the junction of the spike protein-ACE2 interface. Integrating various biological data, Gaussian kernel, similarity kernel, and logistic matrix factorization with kernel diffusion, this work demonstrates that a few chemical agents may assist in drug discovery for COVID-19.