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A (Yb0.05Nd0.003Sc0.947)2SiO5 (Yb3+,Nd3+:Sc2SiO5) single crystal grown by the Czochralski technique is designed to enhance the gain cross-section through the energy transfer between energy level 4F3/2 of Nd3+ ions and energy level 2F5/2 of Yb3+ ions. The cell parameters were calculated as a = 9.94 A, b = 6.29 A, c = 11.67 A, V = 710.67 A3 and β = 103.19 °. The absorption cross-section σ abs in Yb3+,Nd3+:Sc2SiO5 was 1.18 × 10−20 cm2 at 980 nm, which was an increase of 28.3% when compared with that in a Yb3+:Sc2SiO5 crystal. The emission cross-section σ em in Yb3+,Nd3+:Sc2SiO5 was 0.63 × 10−20 cm2 at 1063 nm, an enhancement of 18.9% when compared with that in Yb3+:Sc2SiO5. The minimum pump intensity parameter I min at 1063 nm was 0.39 kWcm−2, which is a 74.5% reduction compared with 1.53 kWcm−2 in the case of YAG. A direct continuous wave diode-pumped Yb3+,Nd3+:Sc2SiO5 laser could generate an output power of 6.14 W at 1057.88 nm with a slope efficiency of 56.7% by using an output coupler with transmission T = 10%.