We describe a new method for evaluating the viscoelastical characterization of biological tissue by photoacoustic technique in this paper. The amplitude attenuation curse of the tissue photoacoustic signals (the stress waves) induced by Q-YAG laser provides necessary data for us to work out the decay time of the stress waves. According to the theory of viscoelasticity, the decay time is equal to the tissue viscosity-elasticity ratio. The result we get from measuring gelatin shows the viscosity-elasticity ratio of Kelvin-Voigt model tissue obtained by photoacoustic measurement almostly equals that by conventional rheometer. The agreement is almost 97%. Furthermore, we firstly apply the method to measure the tissue viscosity-elasiicity ratio of Maxwell model. From the theorical analysis and the experimental result, we can conclude that the method can be applied to any model tissue, because it is only related with its acoustic impedance, having nothing to do with tissue state. In short, photoacoustic measurement is real-time, noninvasive and highly sensitive and repetitive. Based on the virtues mentioned above, it can be widely applied to biology and medicine.