Reinforced cushion and pile are two important components of the geosynthetic-reinforced and pile-supported (GRPS) composite foundation. Studies on the traditional GRPS composite foundation with uniform section piles have compared the performance of GRPS before and after the reinforcement of cushion yet neglects the effects of reinforcement type and pile shape on this composite foundation. To address this problem, the geosynthetic-reinforced and tapered pile-supported (GRTPS) composite foundation with section-variable piles was proposed in this study as a new form of the GRPS composite foundation. The settlement of the proposed composite foundation and the stress distribution on piles and soil under three cushion conditions (gravel cushion (GC), geogrid-reinforced cushion (GGRC), and geocell-reinforced cushion (GCRC)) were analyzed through a static test by using three models of specimens with nine piles. Test results demonstrate that under the test load, the pile-soil settlement differences under GGRC and GCRC are 43.4% to 49.8% and 34.7% to 39.8% of that under GC. Meanwhile, the pile-soil stress ratios under GGRC and GCRC are 1.47 to 1.88 and 1.77 to 2.08 times of that under GC. The reinforced cushion can effectively reduce the settlement of the composite foundation and the pile-soil settlement difference, increase the pile-soil stress ratio, and relieve stress concentration in some piles. GCRC can improve the performance of the GRTPS composite foundation more effectively than GGRC under the same conditions. No negative friction region is observed on the upper piles in the GRTPS composite foundation. The tapered piles are better than the uniform section ones as well as can increase the bearing capacity and decrease the settlement of the composite foundation. The findings of this work can provide references for the engineering design and application of the GRTPS composite foundation.