Investigating the pressure dependence of the superconducting (SC) transition temperature $T_{rm c}$ is crucial for understanding the SC mechanism. Herein, we report on the pressure dependence of $T_{rm c}$ in the nonmagnetic topological line-nodal material CaSb$_2$, based on measurements of electric resistance and alternating current magnetic susceptibility. $T_{rm c}$ initially increases with increasing pressure and peaks at $sim$ 3.1~GPa. With a further increase in pressure, $T_{rm c}$ decreases and finally becomes undetectable at 5.9~GPa. Because no signs of phase transition or Lifshitz transition are observed in the normal state, the peculiar peak structure of $T_{rm c}$ suggests that CaSb$_2$ has an unconventional SC character.
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