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