The present contribution is concerned with the modeling and computation of size effects in metallic glasses. For the underlying model description, we resort to a thermodynamically consistent, gradient-extended continuum mechanics approach. The numerical implementation is carried out with the help of the finite element method. Numerical examples are presented and compared with existing experimental findings to illustrate the performance of the constitutive model. In this regard, the influence of the material length scale is investigated. It is shown that with decreasing sample size or decreasing material length scale, a delay of the shear localization is obtained. In addition, the tension-compression asymmetry observed in experiments is captured by the proposed model. Further, the rate-dependent behavior as well as the influence of the results to initial local defects are investigated.