Highly-efficient high-power fiber lasers operating at wavelength below 1020 nm are critical for tandem-pumping in >10 kW fiber lasers to provide high pump brightness and low thermal loading. Using an ytterbium-doped-phosphosilicate double-clad leakage-channel fiber with ~50 µm core and ~420 µm cladding, we have achieved ~70% optical-to-optical efficiency at 1018 nm. The much larger cladding than those in previous reports demonstrates the much lower required pump brightness, a key for efficient kW operation. The demonstrated 1018 nm fiber laser has ASE suppression of ~41 dB. This is higher than previous reports and further demonstrates the advantages of the fiber used. Limiting factors to efficiency are also systematically studied.