In this paper, a technique combining cascaded energy-transfer pumping (CEP) method and master-oscillator power-amplifier (MOPA) configuration is proposed for power scaling of 1.6-μm-band single-frequency fiber lasers (SFFLs), where the ${\mathrm{Er}}^3$ ion has a limited gain. The CEP technique is fulfilled by coupling a primary signal light at 1.6 μm 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 thanks to the CEP. A single-frequency MOPA laser at 1603 nm with an output power of 52.6 W and an improved slope efficiency of 30.4% is experimentally obtained through the CEP technique. Besides, a laser linewidth of 5.2 kHz and a signal-to-auxiliary laser ratio of 60.7 dB are obtained at the maximum output power. The proposed technique is anticipated to be promising for increasing the slope efficiency and power scaling for fiber lasers operating at L band.