Recently, negative refraction of electromagnetic waves in photonic crystals was demonstrated experimentally and subwavelength imagingobserved. However, these investigations all focused on the periodic structure. Here we report a new theoretical and experimental finding that negative refraction can occur in certain transparent quasicrystalline photonic structures. More interestingly, a superlens based on 2-dimensional photonic quasicrystals can form a non-near-field subwavelength image whose position varies with the source distance. This property makes such quasicrystals promising for application in a range of optical devices.