Image quality assessment algorithms usually lose color information or destroy the structure integrity of image,during the process of assessment,which makes the evaluation results inconsistent with the results of human observation.A no-reference blur red color image quality assessment algorithm is proposed based on QDCT and Bayes spectral entrop y,because the more blurred a image is,the more unevenly distributed these high frequency components are.Firstly,a quaternion matrix is used to represent a color image before it i s divided into non-overlapping sub-matrices of 8×8pixels.Then,the spectrum of each sub-m atrix can be obtained by QDCT.Finally,in order to evaluate the quality of a color image,Bay es spectral entropy is calculated to measure the uniformity of high frequency components in the spectrum. The PLCC and SRCC values of the proposed algorithm on database IVC,TID2013and CSIQ all reach above 0.9202.Experimental data shows that the assessment resu lts of the algorithm in this paper are accurate,stable,and consistent with human subjective observations.