For enhancing the heat storage and encapsulation performances of organic phase change materials (PCMs), a carbon foam (CF) with a continuous dual-scale pore structure (DCF) was developed. Employing the as-prepared DCF as a stearic acid (SA) support, a novel shape-stabilized SA-CF composite PCM with a continuous dual-scale interpenetrating network structure was achieved through the impregnation of SA into the DCF. DCF-900, prepared at an activation temperature of 900 °C, possesses a high loading capacity of 89.54 wt % for melted SA without leakage. The resulting SA/DCF-900 composite with a continuous dual-scale interpenetrating network structure exhibits excellent comprehensive performances with a good synergistic effect. The composite presents a thermal conductivity of 1.298 W/m·K and an encouraging compressive strength of 9.03 MPa, which increase by 2.25-fold and 3.56-fold compared with those of DCF-900, respectively. Furthermore, its melting and freezing enthalpies reach 192.8 and 192.7 J/g with a storage efficiency of about 100%, respectively; meanwhile, it displays excellent thermal cycle stability and reversibility after 600 thermal cycles with a high melting/freezing enthalpy retention rate of up to 96%. More importantly, its light-to-thermal conversion efficiency reaches 91.8% under a light intensity of 100 mW/cm2. Consequently, the SA/DCF-900 composite is a promising candidate for high-performance PCMs.