In this paper, a novel photoacoustic viscoelasticity imaging (PAVEI) technique that provides viscoelastic information of biological tissues is presented. We deduced the process of photoacoustic (PA) effect on the basis of thermal viscoelasticity theory and established the relationship between the PA phase delay and the viscoelasticity for soft solids. By detecting the phase delay of PA signal, the viscoelasticity distribution of absorbers can be mapped. Gelatin phantoms with different densities and different absorption coefficients were used to verify the dependence of PAVEI measurements. Moreover, tissue mimicking phantoms mixed with fat and collagen at different concentrations were used to testify the feasibility of this technique with reliable contrast. Finally, the PAVEI was successfully applied to discrimination between biological tissue constituents. Our experimental results demonstrate that this novel technique has the potential for visualizing the anatomical and biomechanical properties of biological tissues.