A numerical method based on the modified finite-difference time-domain (FDTD) method for calculating and analyzing defect modes in a two-dimensional photonic crystal is presented. An ideal plane wave incident at different angles is realized by using the auxiliary one-dimensional FDTD method and linear interpolation at the total field-scattered field interface. Perfect matched layer technique is employed to absorb the out going wave efficiently. Numerical simulations show that all defect modes can be excited by an incident plane wave along a non-symmetric direction of the photonic crystal. The values of electric field are recorded by choosing a suitable detector position, and all resonant frequencies can be obtained by fast Fourier transform. The relationship between the resonant frequency in a two-dimensional square photonic crystal consisting of dielectric rods and the radius and dielectric constant of the rods is also investigated. The numerical results show that the value of the resonant modes of the photonic crystal can be modulated by changing the radius and dielectric constant.