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In this paper, a novel computationally efficient multiscale framework based on the extended mechanics of structure genome (XMSG) is presented for predicting mechanical properties based on microstructure for Ti6Al4V parts fabricated by additive manufacturing (AM). The XMSG offers its novel capability to account for the effects of microstructure heterogeneity, porosity growth, and crack propagation for the multiscale calculations of the elastic/plastic/damage behavior of the AM parts in a computationally efficient manner. It is shown that XMSG can provide several orders of magnitude improvement in computational efficiency with the same level of accuracy compared to other conventional methods such as representative volume elements. The XMSG framework was applied to predict the tensile and compression behavior of AM Ti6Al4V, which showed very good agreement with the experimental results. In addition, the XMSG framework was able to predict the asymmetry in Young's modulus of the AM Ti6Al4V under tensile and compression loading as well as the anisotropy in the mechanical behavior under tension. • The proposed extended mechanics of structure genome is a novel computationally efficient multiscale homogenization method. • The method is used to successfully predict the mechanical behavior of additive manufactured Ti6Al4V with porosity. • The method is capable of predicting the anisotropy and asymmetry in the mechanical behaviors of Ti6Al4V. • The method is computationally superior to the existing homogenization method by more than two orders of magnitude. [ABSTRACT FROM AUTHOR]