Investigating the pressure dependence of the superconducting (SC) transition temperature Tc is crucial for understanding the SC mechanism. Herein, we report on the pressure dependence of Tc in the nonmagnetic topological line-nodal material CaSb2, based on measurements of electric resistance and alternating current magnetic susceptibility. Tc initially increases with increasing pressure and peaks at ∼ 3.1~GPa. With a further increase in pressure, Tc 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 Tc suggests that CaSb2 has an unconventional SC character.