In this Report, we present a record-high-peak-power single-frequency master oscillator power amplifier (MOPA) system based on a newly developed double-clad large-mode-area Yb-free Er-doped fiber (DC-LMA-EDF). A fiber Bragg grating wavelength-stabilized fiber-coupled diode laser at λ=1551 nm with ~2 MHz spectral width was used as the master oscillator. Its radiation was externally modulated with a 5 kHz repetition rate and 92 ns pulse duration and then amplified in a core-pumped Er-doped fiber amplifier up to an average power of 4 mW. The amplified spontaneous emission (ASE) generated at the last preamplifier stage was suppressed by a narrow-band (0.7 nm) DWDM filter. The last MOPA stage was based on the recently developed single-mode DC-LMA-EDF with a mode field diameter of 25 microns and pump clad-absorption of 3 dB/m at λ=980 nm. The pump and the signal were launched into this fiber through a commercial pump combiner in a co-propagating amplifier scheme. At first, we used a 3-m long DC-LMA-EDF. In such configuration, a peak power of 800 W was achieved at the output of the amplifier together with a ~ 12 % pump conversion slope efficiency. Further power scaling was limited by SBS. After that we shortened the fiber length to 1 m. As a result, owing to large unabsorbed pump power, the efficiency decreased to ~5 %. However, a peak power of more than 3.5 kW was obtained before the SBS threshold. In this case, the pulse shape changed and its duration decreased to ~60 ns owing to inversion depletion after propagation of the forward front of the pulse. To the best of our knowledge, the peak power of more than 3.5 kW reported here is the highest value ever published for a single-frequency single-mode silica-based fiber laser system operating near λ=1550 nm.