The present contribution is concerned with the modelling and computation of stable shear localization process in submicron-sized metallic glasses. To this end, a non-local thermodynamically consistent, continuum mechanical, constitutive model is developed. In our previous work, we formulated the model in the small strain framework. In current work, this model is extended to finite strains. The numerical implementation is carried out with the help of the finite element method. Numerical examples are presented - illustrating the general model behaviour which is correlated to experimental observations. It is shown that the proposed finite deformation model is well suitable to predict the stable shear localization process in submicron-sized metallic glasses and its size effect. The model confirms that with decreasing sample size the shear localization process starts at a later deformation state. Additionally, the finite deformation model is able to predict the failure process in submicron-sized metallic glasses as well as the delay of it with decreasing sample size qualitatively correct.