We have measured the Hall effect in the vortex state of La2-xSrxCuO4 single-crystal thin t-dins from the underdoped to the overdoped regime (x=0.1-0.24). A sign change of the Hall effect is found below Tc in the underdoped and slightly overdoped samples, while it is absent in the overdoped samples. This result is consistent with the theoretical prediction based on the time-dependent Ginzburg-Landan equation, which suggests that the sign reversal is related to the electronic state at the Fermi level.