The formation of supermassive stars (SMSs) via rapid mass accretion and their direct collapse into black holes (BHs) is a promising pathway for sowing seeds of supermassive BHs in the early universe. We calculate the evolution of rapidly accreting SMSs by solving the stellar structure equations including nuclear burning as well as general relativistic (GR) effects up to the onset of the collapse. We find that such SMSs have less concentrated structure than fully-convective counterpart, which is often postulated for non-accreting ones. This effect stabilizes the stars against GR instability even above the classical upper mass limit $gtrsim 10^5~M_odot$ derived for the fully-convective stars. The accreting SMS begins to collapse at the higher mass with the higher accretion rate. The collapse occurs when the nuclear fuel is exhausted only for cases with $dot M lesssim 0.1~M_odot~{rm yr}^{-1}$. With $dot{M} simeq 0.3 - 1~M_odot~{rm yr}^{-1}$, the star becomes GR-unstable during the helium-burning stage at $M simeq 2 - 3.5~times 10^5~M_odot$. In an extreme case with $10~M_odot~{rm yr}^{-1}$, the star does not collapse until the mass reaches $simeq 8.0times 10^5~M_odot$, where it is still in the hydrogen-burning stage. We expect that BHs with roughly the same mass will be left behind after the collapse in all the cases.
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