A potential method to select and generate a single-order harmonic has been proposed and investigated via the waveform control of a frequency-chirping two-color field. It is found that with the combination of two-color chirped pulse, a specific 'W' waveform structure can be found on the falling part of the laser field. Consequently, the accelerated electron in this region will obtain the additional energy due to the multi-acceleration-recombination process and a folded structure on the harmonic emission process can be found. Due to this folded structure, a specific single-order harmonic can be selected and enhanced. Moreover, by properly controlling the laser parameters, the enhancement of the frequency-tunazble single-order harmonic can be achieved. The present results will provide the useful information for the attosecond science community.