When image quality evaluation algorithms are used to evaluate one color image, the color information of the color image is often lost and the integrity is destroyed, which makes the evaluation result inconsistent with the subjective evaluation result. Based on the idea that the more blurred the image is, the less high-frequency components it contains, a no-reference color image quality assessment algorithm is proposed. First, a quaternion matrix is used to characterize the color image and its spectrum can be obtained by quaternion Fourier transform. Then, the threshold value of the high-frequency components is calculated. Finally, the number of pixels above the threshold value is used to calculate the color image quality score. The experimental results show that the predicted results have good accuracy and monotonicity, and match well with the subjective evaluation results. The proposed algorithm has better anti-noise performance, lower computational complexity and better overall performance than existing algorithms.