In this paper, a technique combing cascaded energy-transfer pumping (CEP) method and master-oscillator power-amplifier (MOPA) configuration is proposed for power scaling of 1.6-um-band single-frequency fiber lasers (SFFLs), where the Er3+ ion has a limited gain. The CEP technique is fulfilled by coupling a primary signal light at 1.6 um and a C-band auxiliary laser. The numerical model of the fiber amplifier with the CEP technique reveals that the energy transfer process involves the pump competition and the in-band particle transition between the signal and auxiliary lights. Moreover, for the signal emission, the population density in the upper level is enhanced and the effective population inversion is achieved due to the CEP. A single-frequency MOPA laser at 1603 nm with an output power of 52.6 W is obtained experimentally. Besides, a slope efficiency of 30.4% is improved by more than 10% through the CEP technique. Both the output power and slope efficiency are by far the highest for 1.6-um-band SFFLs. Meanwhile, a laser linewidth of 5.2 kHz and a polarization-extinction ratio of ~18 dB are obtained at the maximum output power. The proposed technique provides an optional method of increasing the slope efficiency and power scaling for fiber lasers operating at L-band.