The voltage-controlled magnetic anisotropy (VCMA) effect is the basis for ultralow-power spin manipulation in spintronic devices such as voltage-controlled magnetoresistive random-access memory (VC-MRAM). A larger VCMA coefficient $\ensuremath{\xi}$ is required to develop VC-MRAM with a higher density. Although $\ensuremath{\xi}$ is theoretically proportional to the dielectric constant ${\ensuremath{\varepsilon}}_{\mathrm{r}}$ of the tunnel barrier material, this relationship has not been experimentally examined. We systematically investigated the relationship between $\ensuremath{\xi}$ and ${\ensuremath{\varepsilon}}_{\mathrm{r}}$ in a ${\mathrm{Fe}}_{80}{\mathrm{B}}_{20}/\mathrm{MgO}/{\mathrm{HfO}}_{2}$ structure prepared by sputtering-based deposition. We successfully controlled ${\ensuremath{\varepsilon}}_{\mathrm{r}}$ while maintaining perpendicular magnetic anisotropy at the ${\mathrm{Fe}}_{80}{\mathrm{B}}_{20}/\mathrm{MgO}$ interface. Both ${\ensuremath{\varepsilon}}_{\mathrm{r}}$ and $\ensuremath{\xi}$ were observed to monotonically increase with ${\mathrm{HfO}}_{2}$, showing a positive correlation between $\ensuremath{\xi}$ and ${\ensuremath{\varepsilon}}_{\mathrm{r}}$. The maximum $\ensuremath{\xi}$ reached \ensuremath{-}92 \ifmmode\pm\else\textpm\fi{} 4 fJ/Vm with ${\ensuremath{\varepsilon}}_{\mathrm{r}}=19.6\ifmmode\pm\else\textpm\fi{}0.3$. This result experimentally demonstrated that the VCMA effect could be enhanced by increasing ${\ensuremath{\varepsilon}}_{\mathrm{r}}$.