AlSi10Mg alloy has been widely used in the aerospace and automotive industries due to its superior physical and mechanical properties. Most AlSi10Mg components possess complicated-geometrical characteristics, such as planar thin wall, lattice structure, curved surface, etc. In recent years, laser-based powder bed fusion (PBF) has emerged as a promising additive manufacturing technique to produce complex AlSi10Mg alloy parts with a high resolution. PBF of curved-surface components exhibit varied heat transfer conditions, challenging post-fabrication processes, and intricate force conditions during mechanical testing owing to their structural inflections and variable cross-sections. Thus, the mechanical properties of the as-built AlSi10Mg parts with curved surfaces should be comprehensively understood to facilitate the adoption of PBF-built curved-surface AlSi10Mg parts in practical engineering applications. This paper systematically investigated the effects of build orientation on the tensile property and microhardness of the PBF-built AlSi10Mg parts with curved surfaces. The results showed that both bending stress and stretching stress contributed to the overall tensile stress of the curved-surface tensile specimens, and the failure always occurred at the peak/valley locations of the sine curved surface due to the largest bending moment. Meanwhile, the ultimate tensile strength increased with the build orientation varying from 60° to 90°. In addition, the curvatures C2 and C4 presented the lowest microhardness while C1 and C5 showed the highest one.