Abstract: Teaching about the theorem of moment of momentum about a moving point is discussed. A few textbooks of theoretical mechanics are investigated in the treatments of different forms the theorem of moment of momentum, including the theorems of moment of momentum about a fixed point, the mass center, and an arbitrary moving point as well as the theorems of moment of relative momentum about the mass center and an arbitrary moving point. Two new derivations of the theorem of the relative moment of momentum about an arbitrary moving point are proposed respectively based on the theorem relative moment of momentum about the mass center and the theorem of moment of momentum about an arbitrary moving point.