Quantum gravity corrections have been speculated to lead to modifications to space-time geometry near black-hole horizons. Such structures may reflect gravitational waves, causing echoes that follow the main gravitational waves from binary black-hole coalescence. By studying two phenomenological models of the near-horizon structures under the Schwarzschild approximation, we show that such echoes, if they exist, will give rise to a stochastic gravitational-wave background, which is very substantial if the near-horizon structure has a near-unity reflectivity for gravitational waves, readily detectable by Advanced LIGO. In case the reflectivity is much less than unity, the background will mainly be arising from the first echo, with a level proportional to the power reflectivity of the near-horizon structure, but robust against uncertainties in the location and the shape of the structure-as long as it is localized and close to the horizon. Sensitivity of third-generation detectors allows the detection of a background that corresponds to power reflectivity ∼3×10^{-3}, if uncertainties in the binary black-hole merger rate can be removed. We note that the echoes do alter the f^{2/3} power law of the background spectra at low frequencies, which is rather robust against uncertainties.