It is extremely significant to study the trap state passivation and minimize the trap states of perovskite to achieve high-performance perovskite solar cells (PSCs). Here, we have first revealed and demonstrated that a novel p-type conductor Cu(thiourea)I [Cu(Tu)I] incorporated in perovskite layer can effectively passivate the trap states of perovskite via interacting with the under-coordinated metal cations and halide anions at the perovskite crystal surface. The trap state energy level of perovskite can be shallowed from 0.35-0.45 eV to 0.25-0.35 eV. In addition, the incorporated Cu(Tu)I can participate in constructing the p-i bulk heterojunctions with perovskite, leading to an increase of the depletion width from 126 to 265 nm, which is advantageous for accelerating hole transport and reducing charge carrier recombination. For these two synergistic effects, Cu(Tu)I can play a much better role than that of the traditional p-type conductor CuI, probably due to its identical valence band maximum with that of perovskite, which enables to not only lower the trap state energy level to a greater extent but also eliminate the potential wells for holes at the p-i heterojunctions. After optimization, a breakthrough efficiency of 19.9% has been obtained in the inverted PSCs with Cu(Tu)I as the trap state passivator of perovskite.