Femtosecond laser-induced air plasma can generate terahertz waves. The sawtooth-like asymmetric photoelectric field can be made by the superposition of three-color laser with appropriate amplitude ratio, frequency ratio and phase difference. Based on the transient photocurrent model and numerical simulation, it is found that intense terahertz waves can be generated by the sawtooth-like asymmetric photoelectric field with different frequency ratios of three-color femtosecond laser, such as 1:2:4 and 1:2:6. By investigating time-varying parameters, such as electron density, electron velocity and photocurrent density, it was further demonstrated that the shape of the asymmetric photoelectric field plays an important role in the formation of net photocurrent and the generation of terahertz waves. The investigation will be helpful to the development of key techniques on intense terahertz waves generated by laser-induced air plasma. © 2019 SPIE.