We demonstrate, to the best of our knowledge, the first cladding-pumped all-fiber oscillator configuration with selective transverse mode generation based on a mode-selective fiber Bragg grating pair. Operating in the second-order (LP11) mode, maximum output power of 4.2 W is obtained with slope efficiency of about 38%. This is the highest reported output power of single higher-order transverse mode generation in an all-fiber configuration. The intensity distribution profile and spectral evolution have also been investigated in this paper. Our work suggests the potential of realizing higher power with selective transverse mode operation based on a mode-selective fiber Bragg grating pair.