The origin of Galactic cosmic rays (CR) is still a matter of debate. Diffusive shock acceleration (DSA) applied to supernova remnant (SNR) shocks provides the most reliable explanation. However, within the current understanding of DSA several issues remain unsolved, like the CR maximum energy, the chemical composition and the transition region between Galactic and extra-Galactic CRs. These issues motivate the search for other possible Galactic sources. Recently, several young stellar clusters (YSC) have been detected in gamma rays, suggesting that such objects could be powerful sources of Galactic CRs. The energy input could come from winds of massive stars hosted in the clusters which is a function of the cluster total mass and initial mass function (IMF) of stars. In this work we evaluate the total CR flux produced by a synthetic population of YSCs assuming that the CR acceleration occurs at the termination shock of the collective wind resulting from the sum of cluster's stellar winds. We show that the spectrum produced by YSC can significantly contribute to energies above ≳ 100 TeV if the diffusion inside the wind-blown bubble is Bohm-like and the spectral slope is harder than the one produced by SNRs.