To develop a cost-effective, high-viscosity asphalt for porous asphalt pavement, we utilized SBS, tackifier, and solubilizer as the main raw materials, identified the optimal composition through an orthogonal experiment of three factors and three levels, and prepared a low-cost high-viscosity asphalt. We compared its conventional and rheological properties against those of rubber asphalt, SBS modified asphalt, and matrix asphalt, employing fluorescence microscopy and Fourier transform infrared spectroscopy for microstructural analysis. The results indicate that the optimal formula composition for high-viscosity asphalt was 4–5% styrene-butadiene-styrene (SBS) + 1–2% tackifier +0–3% solubilizer +0.15% stabilizer. The components evenly dispersed and the performances were enhanced with chemical and physical modification. Compared with SBS modified asphalt, rubber asphalt, and matrix asphalt, the softening point, 5 °C ductility, and 60 °C dynamic viscosity of high-viscosity asphalt were significantly improved, while the 175 °C Brookfield viscosity was equivalent to SBS modified asphalt. In particular, the 60 °C dynamic viscosity reaches 383,180 Pa·s. Rheological tests indicate that the high- and low-temperature grade of high-viscosity asphalt reaches 88–18 °C, and that high-viscosity asphalt has the best high-temperature resistance to permanent deformation and low-temperature resistance to cracking. It can save about 30% cost compared to commercially available high-viscosity asphalt, which is conducive to the promotion and application of porous asphalt pavement.