Matrix completion is a challenging problem in computer vision. Recently, quaternion representations of color images have achieved competitive performance in many fields. The information on the coupling between the three channels of the color image is better utilized since the color image is treated as a whole. Due to this, researcher interest in low-rank quaternion matrix completion (LRQMC) algorithms has grown significantly. In contrast to the traditional quaternion matrix completion algorithms that rely on quaternion singular value decomposition (QSVD), we propose a novel method based on quaternion Qatar Riyal decomposition (QQR). First, a novel approach (CQSVD-QQR) to computing an approximation of QSVD based on iterative QQR is put forward, which has lower computational complexity than QSVD. CQSVD-QQR can be employed to calculate the greatest r(r>0) singular values of a given quaternion matrix. Following that, we propose a novel quaternion matrix completion approach based on CQSVD-QQR which combines low-rank and sparse priors of color images. Furthermore, the convergence of the algorithm is analyzed. Our model outperforms those state-of-the-art approaches following experimental results on natural color images and color medical images.