Organic materials with strong two-photon absorption response and aggregation induced emission have aroused a great deal of interest in recent years, for their many potential applications such as two-photon fluorescence microscopy, up-conversion laser, photodynamic therapy, etc. The tetraphenylethylene units are usually employed in two-photon absorption and aggregation induced emission materials because of their good electron-donating capability and special propeller starburst structures. Theoretical study on the relationship between molecular structure and two-photon absorption property is of great importance for guiding the experimental design and synthesis of functional materials. In this paper, the two-photon absorption properties of a series of organic molecules containing tetraphenylethylene and cyano groups are studied by employing the density functional response theory in combination with the polarizable continuum model. The molecular geometries are optimized at a hybrid B3LYP level with 6-31g(d, p) basis set in the Gaussian 16 program. The two-photon absorption cross sections are calculated by response theory through using the CAM-B3LYP functional with 6-31g(d) basis set in the Dalton program. The effect of donor position and number on two-photon absorption properties are investigated. In addition, by increasing the planarity and conjugated length of the molecule, as well as by enhancing the strength of the electron donor, we design three molecular structures and calculate their two-photon absorption properties. The results show that the donor position and number have important effects on two-photon absorption properties. The methoxy donor at the end of the molecule can increase the two-photon absorption intensity effectively. As the number of substituents increases, the position of the two-photon absorption peak is red-shifted. The effects of adding electron donor groups on different side positions have a significant difference in the two-photon absorption property. Comparing with the experimental molecules, the two-photon absorption cross sections of the designed molecules are greatly enhanced. When the tetraphenylethylene group is replaced by the triphenylamine group, the two-photon absorption peak is greatly red-shifted, and the two-photon absorption intensity is significantly increased. Since all of these molecules contain tetraphenylethylene or triphenylamine group with propeller structure, they can have both two-photon absorption and aggregation induced emission properties. This study provides theoretical guidelines for synthesizing a new type of active two-photon absorption and aggregation induced emission material.