In this work, using perturbation technique we have developed an approximate analytic model for evaluating the band structure of a 2-D octagonal photonic quasicrystal (PQC). Although numerical techniques are being used for evaluating such band structures, developing a numerical model to the best of our knowledge this work is the first instance of reporting helps to understand the physical properties of the structure more easily. Use of perturbation technique can be beneficial in approximating the photonic band structures, in PQCs made with low-dielectric contrast materials, with high accuracy. To the best of our knowledge this work is the first instance of reporting the development of such an analytic model for octagonal PQCs. In addition, we have studied the effect of variations in the dielectric contrast on the photonic band structure.