Optical parametric chirped pulse amplification (OPCPA) is the most promising key technology to achieve the large ultra-high power and ultrashort pulse laser system. However, parametric fluorescence is still an important factor affecting the temporal contrast of the system. We review the theoretical and experimental research of the parametric fluorescence, discuss the mechanism of its generation and point out the parameters which affect the spatial-temporal pattern and spectrum distribution. Based on that, we summarize the suppression of parametric fluorescence in the aspects of the input energy and the saturated or over-saturated amplification. Temporal contrast of the OPCPA system can be improved by the means mentioned above, and it satisfies the requirements of high quality physical experiments.