High-order optical harmonic emission from a single atom exposed in the intense chirped laser pulses has been calculated. Harmonic spectral shifting and broadening are found. Namely, for the negatively chirped pulses, blue-shifting can be observed in the front part (11 st～51 st order) of the harmonic plateau. But the back part from 53rd to 91st harmonic orders occur to red-shift. When the sign of chirp is changed to be positive, the spectral shifting is just reverse. Regardless the sign of chirp every harmonic order is broadened in different degree for different order number. The bandwidths of individual peaks are broad enough to support subfemtosecond pulses if the pertinent phase conditions can be met. These calculation results agree well with the recent experiment performed by Zhou et al. although the opposite spectral shifting in the back part of harmonic plateau is not reported in their experiment. It indicates that a tunable, ultrashort soft X-ray source can be obtained by controlling the degree and sign of chirp.