The apparent mass effect is enhanced significantly when the motion of a body changes quickly, such as a flapping wing or an impulsively started plate. Previous method for calculating the apparent mass of a given body needs to adopt the assumption of ideal flow and know the potential of velocity field arising in the fluid due to the motion of the body. However, the assumption of ideal flow is contrary to real fluid field and it is hard to obtain the potential of velocity field in most cases. In this paper, a new method based on the vorticity moment theorem for calculating the apparent mass of the body of revolution in the axial direction due to axial acceleration is developed. This method has no assumption of ideal flow and establishes the relationship between the apparent mass and the vorticity loops adjacent to the surface of the body. Using this method, the value of the apparent mass can be easily figured out and the physical mechanism of the apparent mass can be revealed from the view of the vorticity loop. The comparisons between different bodies have shown the influences of the fineness ratio (the ratio of the length to the maximum diameter) and the trailing edge type on the apparent mass.