Hollow-core anti-resonant fibers (HC-ARFs) are widely used for high-power laser transmissions owing to their low nonlinearity and high damage threshold. However, most existing structural designs are suitable for single-mode guidance but are inadequate for efficient transmission of few- or multi-mode lasers with high output power. In this study, we fabricated a low-loss multi-mode 8-tube nested hollow-core anti-resonant fiber (Nested HC-ARF) with a minimum loss of 3.27 dB/km at 1 μm wavelength, which enabled the efficient transmission of at least five mode groups. Accordingly, we demonstrated the transmission of a record 3 kW few-mode (M2∼1.38) continuous-wave laser with a maximum transmission efficiency of 95.2% using a 10 m multimode Nested HC-ARF and an optimized transmission system. The experimental verification of the beam quality and spectrum indicated distortion-free transmission, which paves the way to power delivery on the scale of tens of kilowatts.