The Rayleigh-Taylor mixing with a premixed layer is investigated in the present study. A BHR-II turbulence model is employed to simulate the Rayleigh-Taylor mixing with different premixed layers. The implementation of the BHR-II model is described in detail and validated in canonical problems. Afterwards, the classic Rayleigh-Taylor instability (RTI) with a premixed layer is studied. Effects of density ratio, layer thickness and density profiles on the late time behaviour of classic RTI are analysed, and the results are also compared with ILES data. It turns out that the premixed layer delays the transition time of turbulent mixing. The late time behaviours of different premixed cases show a similar trend with the similarity of their distributions of turbulent kinetic energy. It is also shown that the premixed layer has little effect on the tilted angle in the canonical tilted rig case while the temporal evolution of the turbulent mixing at the early beginning is distinctly influenced by the premixed layer.