Nanoparticles (20–50 nm) of Na⁺, CO₃²⁻-containing calcium phosphate (Na: 1.49 wt% and C: 1.53 wt%) with apatite-type structure were prepared by precipitation method from aqueous solution. According to FTIR spectroscopy data, the partial substitution of phosphate by carbonate (B-type) realized in the apatite-type structure. Obtained Na⁺, CO₃²⁻-hydroxyapatite (HAP) was used for the preparation of hybrid biocomposites with Alginate (Alg) with weight ratio HAP: Alg = 1:1 or 2:1 and C₆₀ fullerene (C₆₀; from 0.2 to 4 wt%) and their mechanical properties were determined. It was found, that sample with weight ratio HAP: Alg = 2:1 and containing 4.0 wt% of C₆₀ has the highest Young's modulus 429 MPa comparing with other determined samples. The structure modeling of the investigated system showed that the formation of triple complexes Na⁺, CO₃²⁻-HAP–Alg–C₆₀ is stabilized by solvophobic and stacking interactions. The created biocomposites can be used as an effective implant material for bone restoration.