We propose and experimentally demonstrate an effective spectral linewidth suppression scheme for a commercial tunable laser source. By using a long-cavity, narrow-bandwidth stimulated Brillouin scattering filter and multifrequency-selection mechanism simultaneously, a single-longitudinal-mode laser output with linewidth suppression from ~3 MHz to less than 20 kHz is successfully achieved in the whole C-band. Meanwhile, insertion loss of ~5 dB and a side-mode suppression ratio improvement of ~20 dB at a typical output wavelength of 1552.520 nm are obtained. The scheme is experimentally verified to be wavelength independent in the C-band and characterized with good performance of wavelength and power stability.