As a new color image representation tool, quaternion has achieved excellent results in color image processing problems. In this paper, we propose a novel low-rank quaternion matrix completion algorithm to recover missing data of a color image. Motivated by two kinds of low-rank approximation approaches (low-rank decomposition and nuclear norm minimization) in traditional matrix-based methods, we combine the two approaches in our quaternion matrix-based model. Furthermore, the nuclear norm of the quaternion matrix is replaced by the sum of the Frobenius norm of its two low-rank factor quaternion matrices. Based on the relationship between the quaternion matrix and its equivalent complex matrix, the problem eventually is converted from the quaternion number domain to the complex number domain. An alternating minimization method is applied to solve the model. Simulation results on color image recovery show the superior performance and efficiency of the proposed algorithm over some tensor-based and quaternion-based ones.