A fuel injection amount control apparatus of an internal combustion engine is arranged to start injection of a fuel into an intake passage of the engine when a certain engine start condition is satisfied, and stop the injection of the fuel when a certain engine stop condition is satisfied. The control apparatus estimates an amount of fuel deposited on an intake passage forming member that defines the intake passage, and determines a fuel injection amount based on the estimated fuel deposition amount. The control apparatus also executes a particular process for making an actual fuel deposition amount on the intake passage forming member substantially equal to zero, after the engine stop condition is satisfied and before the injection of the fuel is started under a condition that the engine start condition is satisfied.