Atomistic simulation is applied to investigate the tension-compression (T-C) asymmetry of the nanotwinned Au nanowires (NTWs) with the different twin orientations in this paper. The result demonstrates that the T-C asymmetry is not only represented by the different yield stress under tensile and compressive load, namely yield asymmetry, but also highlighted by the different strengthening effect of twin boundaries, namely strengthening asymmetry. The yield asymmetry in the NTWs becomes weaker than that in their single-crystal counterparts and highly twin orientation-dependent. In more details, the compressive yield stress is larger than the tensile yield stress when the twin orientation angle is 0 degrees, 19.47 degrees and 90 degrees, while the opposite is true as the twin orientation angle changes to 54.74 degrees. The strengthening effect is much obvious under tensile load in the NTW with a twin orientation angle of 0 degrees, while no significant difference is found in the NTW with a twin orientation angle of 90 degrees. In contrast, the NTWs with a twin orientation angle of 19.4T and 54.74 degrees exhibit great reduced tensile and compressive strength. This work not only deepens our understanding of the mechanical behavior of the nanotwinned metal but also provides a new strategy to control mechanical behavior via nanotwin boundaries design.