The nanoinstability of single-wall carbon nanotubes(SWCNT) under electron beam irradiation is systematically investigated by in-situ transmission electron microscopie observation at room temperature. Under the same irradiation condition, it is found that with the increasre irradiation time(or electron dose), the SWCNT whose two ends are fixed at ropes of nanotubes shrinks in its radial direction with an increasingly faster rate; the curved SWCNT is more instable than the straight one with a the same diameter; the SWCNT with a free capped end but the other end fixed at a rope of nanotubes shrinks in the axial direction but almost keeps its diameter unchanged. All experimental phenomena could be well accounted for by new concepts of vaporing and diffusing of carbon atoms as strongly driven by the nanocurvature of SWCNT as well as by the electron beam-induced athermal activation.