The second-generation high-temperature superconductor (2G HTS) is a good candidate for high field magnet due to its high critical temperature Tc,high critical current density Jc,and high irreversibility field Hirr.This paper presents the design and development of a 4.08 T (46 K) coil made of homemade 2G HTS.In order to meet the design requirement of HTS coil,the electromagnetic finite element modeling and optimization are carried out on the basis of the research of the properties of YBa2Cu3O7-x(YBCO) tapes.And the design scheme of HTS coil is completed.Then the HTS coil with an inner diameter of 100 mm is successfully constructed according to the scheme.It consists of a stack of 10 double-pancakes with the same outer diameter wound with YBCO tapes.The diameter and height of the HTS coil are 236 and 359 mm,respectively.A total of 1600 meters of YBCO tape are used to wind this HTS coil.We measure the I-V curves of superconducting coil at different cryogenic temperatures.First,liquid nitrogen is used to cool the HTS coil to 77 K,and then the temperature is reduced to 65 K by the decompression cooling method.The cooling coil containing liquid helium is used to exchange heat and cool the solid nitrogen to obtain much lower cryogenic temperature.The maximum operating currents of the HTS magnet at 77,65,and 55 K are 65,147,and 257 A,respectively,corresponding to the center magnetic field of 0.78,1.77,and 3.1 T.At 46 K,the HTS coil with an inner diameter of 100 mm generates a 4.08 T field at the center.And the magnetic field of superconducting coil is basically uniform in the medium plane.The results demonstrate a strong potential of home-made YBCO magnet for direct current high-field applications.