Raman spectra of Sr_14-xCa_xCu₂₄O₄₁ in single-crystal and polycrystalline samples were investigated. At first, from the polarization and a comparison with previous reports on isostructural compounds, we identify the (4A_g+4B_1g+3B_2g+B_3g) modes that are Raman active within the simple Fmmm structure. Second, it is clear that hole carriers transfer from chain to ladder with substituting Sr for Ca in Sr₁₄Cu₂₄O₄₁, because on the one hand the intensity for modes associated with oxygen vibrations for chain increases and on the other hand the one associated with ladder decreases with Ca content x increasing. Third, we observe new additional modes at low temperature in this system. Especially, for both Sr₁₄Cu₂₄O₄₁ and Sr_7.2Ca_6.8Cu₂₄O₄₁, the temperature, at which the new mode near 500 cm-1 shows up, is nearly identical to the temperature, at which the electrical and magnetic anomalies have been observed. This result is consistent with the picture that holes in the ladder are paired and localized below the temperature.