The research on boundary-layer receptivity is the key issue for the laminarturbulent transition prediction in fluid mechanics. Many of the previous studies for local receptivity are on the basis of the parallel flow assumption which cannot accurately reflect the real physics. To overcome this disadvantage, local receptivity in the non-parallel boundary layer is studied in this paper by the direct numerical simulation (DNS). The difference between the non-parallel and parallel boundary layers on local receptivity is investigated. In addition, the effects of the disturbance frequency, the roughness location, and the multiple roughness elements on receptivity are also determined. Besides, the relations of receptivity with the amplitude of free-stream turbulence (FST), with the roughness height, and with the roughness length are ascertained as well. The Tollmien- Schlichting (T-S) wave packets are excited in the non-parallel boundary layer under the interaction of the FST and the localized wall roughness. A group of T-S waves are separated by the fast Fourier transform. The obtained results are in accordance with Dietz's measurements, Wu's theoretical calculations, and the linear stability theory (LST).