A phase field model is established to investigate the surface-energy-driven abnormal grain growth in thin films. It is consistent with sharp interface model and its parameters are connected to material properties. Numerical simulations show that surface energy anisotropy and drag effect are required to motivate the abnormal grain growth. The size of a single abnormal grain increases linearly as a function of time, and it exhibits power-law scaling with film thickness and Arrhenius relationship with temperature. For multiple abnormal grains, their area fraction can be characterized by the Avrami equation with exponent around 2 at large times. These features agree well with the theoretical and experimental results.