Multiple hard and semi-hard parton scatterings in high-energy $p+A$ collisions involve multi-parton correlation in both momentum and flavor inside the projectile proton which will lead to modification of the final hadron spectra relative to that in $p+p$ collisions. Such modification of final hadron transverse momentum spectra in $p+A$ collisions is studied within HIJING 2.1 Monte Carlo model which includes nuclear shadowing of the initial parton distributions and transverse momentum broadening. Multi-parton flavor and momentum correlation inside the projectile are incorporated through flavor and momentum conservation which are shown to modify the flavor content and momentum spectra of final partons and most importantly lead to suppression of large $p_{T}$ hadron spectra in $p+A$ collisions at both RHIC and LHC energies.