The vorticity equation in the form of momentum cross multiplication is derived in pressure coordinate, in which the divergence term in the classic vorticity equation （CVE） does not appear. This vorticity equation in momentum cross multiplication form involves the rotation effect of the horizontal wind advection, which can be called the advective vorticity equation （AVE）. Because the rotational effect of horizontal wind advection can be directly analyzed on the synoptic charts, this equation is easily applied to operational weather analysis. The vorticity and its tendency of typhoon Bilis occurred in July 2006, it is analyzed and the results show that the distributions of the vertical vorticity tendencies from the two equations are similar except that the values of AVE is larger than that of CVE, and positive vorticity tendency from AVE is more concentrated than that of CVE. The detailed analyses of the three terms on the right hand side of AVE indicated that the advective term is a leading factor in determining the change of vertical vorticity for the development of the typhoon Bilis. When the vorticity induced by the rotational effect of horizontal wind advection plays a dominant role, AVE shows advantages for the diagnosis and analysis of synoptic systems. Thus, the AVE is useful for analysis of the change of vorticity and diagnosis of the movement for typhoon Bilis. Furthermore, the tendency of the term related to geostrophic vorticity and divergence always accords with the track of Bilis, which means this term can be used as an indicator for track prediction of typhoon.