A unified model of the L-mode confinement in tokamaks and the improved modes associated with current profile modification is investigated by means of a one-dimensional transport simulation. The thermal transport coefficient employed is based on the theory of self-sustained turbulence due to the current-diffusivity-driven modes. In the case of low beta p ( beta p being the ratio of the plasma pressure to the pressure of the poloidal magnetic field), the simulation results show fairly good agreement with empirical L-mode scaling laws of the thermal energy confinement time tau E, indicating favourable dependence on the plasma current. When beta p exceeds about unity, however, the transport in the core region is strongly reduced. This confinement improvement is attributed to the weak or negative magnetic shear due to the bootstrap current and the Shafranov shift of the magnetic surface. The enhancement factor of tau E scales as beta p0.76 and is consistent with experimental observation. The effect of current profile modification due to the current ramp down and the lower hybrid current drive is also studied.