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High dielectric constant polymers have been widely studied and concerned in modern industry, and the induction of polar groups has been confirmed to be effective for high permittivity. However, the way of connection of polar groups with the polymer backbone and the mechanism of their effect on the dielectric properties are unclear and rarely reported. In this study, three polyimides (C0-SPI, C1-SPI, and C2-SPI) with the same rigid backbone and different linking groups to the dipoles were designed and synthesized. With their rigid structure, all of the polyimides show excellent thermal stability. With the increase in the flexibility of linking groups, the dielectric constant of C0-SPI, C1-SPI, and C2-SPI enhanced in turn, showing values of 5.6, 6.0, and 6.5 at 100 Hz, respectively. Further studies have shown that the flexibility of polar groups affected the dipole polarization, which was positively related to the dielectric constant. Based on their high permittivity and high temperature resistance, the polyimides exhibited outstanding energy storage capacity even at 200 °C. This discovery reveals the behavior of the dipoles in polymers, providing an effective strategy for the design of high dielectric constant materials.