A strong blueshift of high-order harmonics was observed when intense femtosecond Ti:sapphire laser pulses were applied to Ar and Ne. The blueshift was systematically investigated for various experimental parameters, such as laser intensity, laser-pulse duration, and gas density. We observed the harmonic blueshifts of two times the laser frequency in the 39th harmonic from Ar and four times the laser frequency in the 85th harmonic from Ne. A semiclassical calculation predicted the inverse proportionality of the blueshift to the laser-pulse duration, which was confirmed in the experiment done with 30 fs and YB fs pulses. The density dependence of blueshift showed that the self-phase modulation in an ionizing medium was not a major factor of the observed blueshift. The experimental results along with theoretical calculations confirmed that the observed blueshift resulted mainly from the nonadiabatic effect due to the rapid increase in the femtosecond laser electric field.