Our universe is fulfilled by stochastic background of gravitational waves with a large range of frequencies, which may have various astrophysical/cosmological origins in the early universe. As our universe is transparent to gravitational wave, it is a fossil recording the information of its generation and how our universe evolves. In this talk I will briefly review the stochastic background of the gravitational waves from the nonlinear coupling of the scalar and tensor perturbations, as well as their connection to the primordial black holes. I will also talk about the properties of the spectrum shape of such waves: infrared scaling and the peak width.