Laser induced air-plasma is a simple and convenient source to generate intense terahertz (THz) waves through the ionization of gaseous molecules. However, the lack of enhancement and efficient frequency modulation methods for this source hinders its widespread application. Recently, we have shown that the two crossed two-color air-plasmas can significantly increase the THz wave generation or select the required THz emissions under the suitable time delay between the two identical ones (the same intensities of the two-color lasers and the same relative phase between them). In the latest research, we change one of the input laser pulses to generate the two crossed air-plasmas from the twocolors (800 nm + 400 nm) to only the single 800 nm. Interestingly, unlike the results we reported in our previous paper, no spectral interference fringe is observed in the THz spectrum, suggesting that it exhibits no interference between THz waves radiated from single-color and two-color laser generated filaments. For THz waves radiated by single-color laser generated plasma, both the absorption and radiation are related to the plasma frequency. However, the THz waves generated from the two-color laser fields appear to be quite different from the single-color one, thus leading to the absence of spectral interference. Research into the underlying mechanisms will reveal more on the plasma-based THz technology, promising to increase the THz intensity yield and deepening our understanding of the ultrafast dynamics.