The turbine blade leading edge is subjected to harsh conditions due to high heat loads and unfavorable compact structures. To improve the cooling performance, a novel impingement scheme is proposed to be used in a film-cooled turbine blade leading edge. Different from a normal impingement scheme, the novel scheme consists of two rows of staggered impinging jets at oblique angles of ±35 deg, and is thus named as the staggered-oblique impingement scheme. A conjugated numerical investigation is carried out to illustrate the underlying mechanisms of the cooling performance. Three typical jet Reynolds numbers, 6000, 12,000, and 18,000, are studied using the validated SST k–ω turbulence model. Numerical results show a flow separation within the staggered-oblique impinging jets, which causes the discharge coefficient for the novel impingement scheme lower than that for the normal impingement scheme. Results also reveal a phenomenon difference that two symmetric vortices are induced by each normal impinging jet, while only one vortex appears on the acute angle side along with each staggered-oblique impinging jet. The flow fields of the staggered-oblique impingement scheme create a more uniform heat transfer distribution and a maximum of 23.7% higher area-averaged Nusselt number than the normal impingement scheme. The area-averaged overall cooling effectiveness for the staggered-oblique impingement scheme is higher than the normal impingement scheme by a maximum of 4.8%. The uniformity and the enhancement of the overall cooling effectiveness arise from the wall jet being fully developed and affecting a larger area of the target wall. The adiabatic cooling effectiveness is similar for both impingement schemes. This indicates that the improvement in overall cooling effectiveness for the staggered-oblique impingement scheme mainly arises from internal heat transfer.