We experimentally demonstrate a stabilized singlefrequency Brillouin fiber laser operating at 1.06 µm by means of a passive highly nonlinear fiber (HNLF) ring cavity combined with a phase-locking loop scheme. The stimulated Brillouin scattering efficiency is first investigated in distinct single-mode germanosilicate core fibers with increasing GeO 2 content. The most suitable fiber, namely 21 mol.% GeO 2 core fiber, is used as Brillouin gain medium in the laser cavity made with a 15-m-longsegment. A Stokes lasing threshold of 140 mW is reported. We also show significant linewidth narrowing (below 1-kHz) as well as frequency noise reduction compared to that of the initial pump in our mode-hop free Brillouin fiber laser.