The author proposes here a new vorticity transfer theory whose fundamental form is τR=-ζ/2D lα²v'd²u/dy², where τ R is Reynolds stress, l the mixture length, α²d²u/dy² the circulation arround turbulent fluid particle and D the distance between the particle and its image refered to wall surface. Effect of viscosity is introduced as a loss of vorticity which appears in the expression of v' . As an application of the theory the flows through circular pipe are calculated, and the result shows a good coincidence with experiment especially in the neighbourhood of wall. The theory can also explain the reason for variation of coefficient of correlation.