To further improve the color image denoising algorithm in quantum image processing, a quantum color image filtering method based on quantum vector median calculation is proposed. The method uses quantum entanglement to bind neighbor pixels and central pixel to the same position to avoid quantum convolution, and introduces the complement code into the quantum circuit to simplify the quantum circuit for vector distance calculation. In addition, a quantum circuit of vector median extraction is designed by using one-time comparison and two-time exchange. Thereby, a complete quantum circuit of the vector median filtering is constructed. Relevant experimental indicators show that the proposed approach has the same noise suppression effect on color salt and pepper noise as the classical vector median filtering, but the time complexity is reduced from $O\left({\mathrm{2}}^{\mathrm{2}n}\right)$ of the classical vector median filtering algorithm to $O(\mathrm{10}{n}^{\mathrm{2}}+\mathrm{216}{q}^{\mathrm{2}})$ of the proposed algorithm.