In order to meet the needs of low-impact development and sustainable development, there is an urgent desire to develop an innovative recycled aggregate pervious concrete (I-RAPC) that is of high strength and permeability. In this study, I-RAPC was prepared based on response surface methodology (RSM) using recycled aggregate, river sand, and different types of pipes as the materials, and the effects of different pipe parameters (number, diameter, material, and distribution form) on the performance of I-RAPC were investigated. In addition, the calculation model of the compressive strength and the permeability coefficient of I-RAPC were proposed. The results showed that the frontal- and lateral-compressive strengths of I-RAPC were 39.8 MPa and 42.5 MPa, respectively, when the pipe material was acrylic, the position was 1EM, and the diameter was 10 mm—at which time the permeability coefficient was 3.02 mm/s, which was the highest in this study. The maximum relative errors of the compressive strength calculation model and the permeability coefficient calculation model were only 7.52% and 4.42%, respectively, as shown by the post hoc test. Therefore, I-RAPC has the advantages of high strength and permeability and is expected to be applied in low-impact development in cities with heavy surface sediment content and rainfall.