In order to improve the gain and directionality of terahertz communication antenna, a cross-like rings stacked lens antenna was proposed in terahertz atmospheric transmission I window. The lens antenna was consisted of a diagonal horn antenna and a multilayer stacked lens. The diagonal horn antenna was adopted as the primary feed and the multilayer comprised cross-like rings. Far field characteristics of the lens antenna was studied by using Fresnel-Kirchhoff diffraction theory and paraxial approximation. Furthermore, the effects of the full-wave period and the focus diameter ratio on radiation characteristics were analyzed by using variable-controlling approach. The proposed lens antenna was fabricated and experimentally tested. The results show that the proposed lens antenna has common processing methods and axisymmetric radiation patterns. The gain is over 26.4 dB and the 3 dB main lobe beamwidth is lower than 4.8° throughout the whole operation bandwidth from 320 to 380 GHz. The good focusing characteristics and great directionality indicate that the designed lens antenna is qualified for applications in THz wireless communication systems.