The invention discloses new long-acting GLP-1 (glucagonlike peptide-1) compounds, a medicine composition containing the compounds, wherein the compound is used for (1) treatments of hyperglycemia, type 2 diabetes, type 1 diabetes, impaired glucose tolerance, obesity, hypertension, X syndrome, dyslipidemia, cognitive disorder, myocardial infarction, coronary heart disease and other vascular diseases, apoplexy, dyspepsia and gastric ulcer, (2) or reducing food intake and beta-cell apoptosis, enhancing beta-cell function and beta-cell quantity , and or, recovering the glucose sensitivity of beta-cell.