We present a new effective permittivity (EP) model to accurately calculate surface plasmons (SPs) using the finite-difference time-domain (FDTD) method. The computational representation of physical structures with curved interfaces causes inherent errors in FDTD calculations, especially when the numerical grid is coarse. Conventional EP models improve the errors, but they are not effective for SPs because the SP resonance condition determined by the original permittivity is changed by the interpolated EP values. We perform FDTD simulations using the proposed model for an infinitely-long silver cylinder and gold sphere, and the results are compared with Mie theory. Our model gives better accuracy than the conventional staircase and EP models for SPs.