A kHz-order linewidth controllable 1550 nm single-frequency fiber laser (SFFL) is demonstrated for the first time to our best knowledge. The control of the linewidth is realized by using a low-pass filtered white Gaussian noise (WGN) signal applied on a fiber stretcher in an optical feedback loop. Utilizing WGN signals with different signal amplitudes An and different cutoff frequencies fc, the linewidths are availably controlled in a wide range from 0.8 to 353 kHz. The obtained optical signal-to-noise ratio (OSNR) is more than 72.0 dB, and the relative intensity noise (RIN) at frequency greater than 40 MHz reaches -148.5 dB/Hz which approaches the shot noise limit (-152.9 dB/Hz). This kHz-order linewidth controllable SFFL is meaningful and valuable, for optimizing the receiver sensitivity and bit error rate (BER) performance of the coherent optical communication system based on high-order quadrature amplitude modulation (QAM).