We report one-dimensional ternary photonic crystals containing a single defect layer, whose photonic band-gap properties including the bandwidth and defect mode are analysed by changing the thickness and position of the defect layer, the number of unit cell repetitions in photonic crystals and the initial incidence angle. The results obtained show that the defect layer thickness can strongly affect the transmittance and the number of defect modes. The defect mode can disappear by increasing the number of periodic layers. The position of the defect layer in the photonic crystals can change the wavelength and transmittance of the defect mode. In addition, both the bandwidth and the defect mode properties of TE and TM waves are strongly dependent on the incidence angle