The present invention discloses four 
crystal forms of a JAK inhibitor N-(5-(4-(1,1-dioxothiomorpholinyl)methyl)phenyl)-[1,2,4]triazolo[1,5-a]pyridin-2-yl)cyclopropanecarboxamide, and methods for preparing the four 
crystal forms, wherein the four 
crystal forms respectively are a crystal form H1, a crystal form H2, a crystal form H3 and a crystal form H4, the crystal form H1 has the characteristic absorption peaks when the 
diffraction angle 2[theta] is 8.3 DEG, 11.2 DEG, 16.0 DEG, 17.5 DEG, 18.5 DEG, 19.3 DEG, 19.7 DEG, 20.0 DEG, 20.7 DEG, 22.0 DEG and the like, the crystal form H2 has the characteristic absorption peaks when the 
diffraction angle 2[theta] is 9.3 DEG, 12.8 DEG, 14.0 DEG, 16.4 DEG, 18.7 DEG, 20.5 DEG, 23.5 DEG, 29.4 DEG, 33.1 DEG, 33.4 DEG and the like, the crystal form H3 has the characteristic absorption peaks when the 
diffraction angle 2[theta] is 9.6 DEG, 9.8 DEG, 10.7 DEG, 15.1 DEG, 15.3 DEG, 16.8 DEG, 16.9 DEG, 19.8 DEG, 20.0 DEG, 24.9 DEG and the like, and the crystal form H1 has the characteristic absorption peaks when the diffraction angle 2[theta] is 8.6 DEG C, 9.6 DEG, 10.5 DEG, 12.9 DEG, 15.1 DEG, 17.2 DEG, 18.9 DEG, 19.9 DEG, 20.7 DEG, 23.8 DEG and the like. According to the present invention, the four crystal forms have advantages of excellent physical and chemical properties, good stability, simple preparation operation and the like, are suitable for 
pharmaceutical formulation applications.