Air-breathing hypersonic vehicles with the head intake system typically cruise at a specific angle of attack for higher lift-to-drag characteristics. However， this can cause the 3D inward-turning inlet， designed without considering the angle of attack， to operate at off-design conditions for extended periods， which results in a noticeable decline in inlet performance. To solve this problem， the Local-Turning Osculating Cones （LTOCs） method is extended from external flow to internal flow， and a 3D inward-turning inlet design method considering the cruising angle of attack is then proposed. In this method， the inward-turning inlet is divided into the shock-based and pressure-based segments， derived by specifying the incident 3D shock wave and the streamwise wall pressure distributions in each stream surface respectively. Numerical results demonstrate that the proposed method can accurately reproduce the preassigned shock waves and internal flowfield at Mach number 6， 27 km altitude， and 4° angle of attack， resulting in full mass flow capture. Compared with the inlet design without considering the angle of attack， the design considering the cruising angle of attack can improve the inviscid mass-flow-capture coefficient and the inviscid total pressure recovery coefficient at the throat section by 1.94% and by 6.56%， respectively， when the compression performances of two inlets are essentially identical. Under the viscous conditions， the mass-flow-capture coefficient is augmented by 1.90%， the total pressure recovery coefficient at the throat section is enhanced by 6.69%， and the total pressure recovery coefficient at the isolator’s exit section is elevated by 7.13%.