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We report X-ray diffraction patterns and calculated electronic band structures of the Dirac line-nodal material CaSb$_2$ under pressure. Its superconducting transition temperature ($T_{\mathrm{c}}=1.7$ K) increases under pressure and reaches a maximum at 3.4 K at around 3 GPa. We observed subtle anomalies in lattice parameters accompanied by a jump in bulk modulus without any change in crystal symmetry at around 3 GPa. First-principles calculations revealed that the distorted lattice of Sb(1) site deforms in the pressure range of 0-3 GPa. Those results suggest the existence of a first-order structural transition and arouse expectations for unusual phononic properties affecting the superconducting state. The calculated pressure dependence of the electronic density of states (DOS) confirms that it is not the change in the DOS that governs the variations in $T_{\mathrm{c}}$.