In this paper, we present a compact model of the spintronic memristor based on the magnetic-domain-wall motion mechanism for circuit design. Our model also takes into account the variations of material parameters and fabrication process, which significantly affects the actual electrical characteristics of a memristor in nano-scale technologies. Our proposed model can be easily implemented by Verilog-A languages and compatible to SPICE-based simulation. Based on our model, we also show some potential applications of memristor in computing system, including the detailed analysis and optimizations based on our proposed model.