The invention provides a large-radius chamfer sleeper used for controlling concrete cracks of a ballastless track and a construction method. In the large-radius chamfer sleeper, (1), large-radius chamfers are used for the corners of the sleeper, the chamfer part is equivalent to a quarter of a circular platform, and the radius of the top of the circular platform is generally not less than 80mm; (2), crack-proof steel bars are arranged on the periphery of the sleeper, wherein the crack-proof steel bars can be arranged to form a closed loop along the outer side of the sleeper or to form loops only in certain ranges of the ends of the sleeper, and ribbed steel bars with nominal diameters being 14mm-20mm are utilized as the crack-proof steel bars; (3), when the grade of the carbonation environment effect is T2, the thicknesses of the protection layers of the crack-proof steel bars are 35mm, and when the grade of the carbonation environment effect is T3, the clear spacings between the crack-proof steel bars and the sleeper are 20mm-30mm; (4), during the construction of the large-radius chamfer sleeper, fixing position accuracy in the whole track bed and soundness of the crack-proof steel bars need to be guaranteed, and meanwhile, the crack-proof steel bars need to be separated from other steel bars.