Single-mode larger-mode-area (LMA) all-glass (free of air-holes) fibers are required for all-fiber high-power lasers and amplifiers as they allow for efficient splicing with other components, which is impossible in the case of LMA photonic crystal fiber. Recently, we have demonstrated an active all-glass Bragg fiber with a mode-field diameter of 26 µm (λ=1.04 µm) [1]. Single-mode transverse mode-oscillation was achieved both in the straight and in the bent fiber (at bend radii larger than 7.5 cm) owing to differential mode gain. In this communication, we propose a Bragg fiber design including a microstructured core in order to increase further the mode-field diameter.