By employing the imaginary time functional technique and the so-called replica method, a quantum vector spin glass model with random Dzyaloshinskii-Moriya anisotropy and ferro-magnetic interaction is investigated for any spin quantum numbers. In the static replica sym-metry limit, the spin self-interaction order parameters, the spin glass order parameters and the magnetization are all determined self-consistently. The relation between susceptibility tensors and order parameters is set up. Compared with other methods, our theory works at all tempe-ratures.