A novel ultra-broadband high-gain antipodal Vivaldi antenna is designed with a bandwidth of 3.3-40 GHz frequency.The same radiation structure, which consists of one microstrip line and two exponential slot lines, is printed on both sides of the dielectric plate.In order to effectively constrain the surface current in the radiation direction, a trapezoidal dielectric substrate is added in the radiation direction, which can not only correct the gain peak offset angle of E-plane pattern, but also improve the radiation intensity of antenna.The measured results show that the VSWR (Voltage Standing Wave Ratio) is smaller than 2 at the frequency band of 3.3-40 GHz, the frequency doubling bandwidth is up to 12, and the gain is 1.0-12.6 dB.In addition, the antenna has the characteristics of good symmetry in E-plane pattern, small cross-polarization ratio, simple structure, easy processing and low cost, thus it has high research significance and application prospects in antenna with high bandwidth and high gain.