A phase field model is presented to capture the formation of a solid electrolyte interface (SEI) layer on the anode surface in lithium ion batteries. In this model, the formation of an SEI layer is treated as a phase transformation process where the electrolyte phase is transformed to the SEI phase due to electrochemical reactions at the SEI/electrolyte interface during SEI growth. Numerical results show that SEI growth exhibits a power-law scaling with respect to time and is limited by the diffusion of electrons across the SEI layer. It is found that during SEI growth, the gradients of both electric potential and concentrations of species are built inside of the SEI layer, and the charge separation at the SEI/electrolyte interface remains with decreasing charge density at the interfacial region. The effects of various factors such as initial conditions, electron diffusivity, SEI formation rate, applied current density and temperature on the SEI growth rate and the distribution of electric potential and concentrations of species are investigated. The capabilities of the present model and its extension are also discussed.