Based on the pair diffusion model that phosphorus in silicon diffuses only via the diffusion of E centers and on the assumptions that the vacancy formation energy decreases with an increase in the phosphorus concentration and that the binding energy between a vacancy and a phosphorus atom is constant, phosphorus diffusion equations are obtained. P+, V+, V0, V-, V-, E0 and E- (P, V and E denote a phosphorus atom, a vacancy and an E center respectively and a superscript denotes the charge state.) are taken into account in the equations. Choosing parameters suitably, anomalies in the phosphorus diffusion, that is, a kink and a tail, are well explained.