In this work, we consider the stochastic background of gravitational waves (SBGWs) produced by pre-galactic stars, which form black holes in scenarios of structure formation. The calculation is performed in the framework of hierarchical structure formation using a Press–Schechter-like formalism. Our model reproduces the observed star formation rate at redshifts z≲ 6.5. The signal predicted in this work is below the sensitivity of the first generation of detectors but could be detectable by the next generation of ground-based interferometers. Specifically, correlating two coincident advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors (LIGO III interferometers), the expected signal-to-noise ratio (S/N) could be as high as 90 (10) for stars forming at redshift z≃ 20 with a Salpeter initial mass function with slope x= 0.35 (1.35), and if the efficiency of generation of gravitational waves, namely, εGW is close to the maximum value ∼7 × 10−4. However, the sensitivity of the future third generation of detectors as, for example, the European antenna EGO could be high enough to produce S/N > 3 same with εGW∼ 2 × 10−5. We also discuss what astrophysical information could be derived from a positive (or even negative) detection of the SBGWs investigated here.