The transmission properties of electromagnetic wave (EMW) can be modulated by the periodic structure of photonic crystal (PhC) to bring many novel optical effects. The special distributions of equal frequency contours (EFCs) can be used to control the wavefront state and transmission direction of propagating wave in PhC with some special effects, such as non-handed refraction. Based on the intricate undulation of one single band or the overlap of different bands, the phenomena of dual-negative refraction, symmetrical positive-negative refraction and triple refraction have been achieved in the higher band regions. These unique features will provide us with more understanding of electromagnetic wave propagation in PhCs and give important guideline for the design of new type optical devices.