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We introduce a novel recursive process to a neural-network-based subgrid-scale (NN-based SGS) model for large eddy simulation (LES) of high Reynolds number turbulent flow. This process is designed to allow an SGS model to be applicable to a hierarchy of different grid sizes without requiring an expensive filtered direct numerical simulation (DNS) data: 1) train an NN-based SGS model with filtered DNS data at a low Reynolds number; 2) apply the trained SGS model to LES at a higher Reynolds number; 3) update this SGS model with training data augmented with filtered LES (fLES) data, accommodating coarser filter size; 4) apply the updated NN to LES at a further higher Reynolds number; 5) go back to 3) until a target (very coarse) filter size divided by the Kolmogorov length scale is reached. We also construct an NN-based SGS model using a dual NN architecture whose outputs are the SGS normal stresses for one NN and the SGS shear stresses for the other NN. The input is composed of the velocity gradient tensor and grid size. Furthermore, for the application of an NN-based SGS model trained with one flow to another flow, we modify the NN by eliminating bias and introducing leaky rectified linear unit function as an activation function. The present recursive SGS model is applied to forced homogeneous isotropic turbulence (FHIT), and successfully predicts FHIT at high Reynolds numbers. The present model trained from FHIT is also applied to decaying homogeneous isotropic turbulence, and shows an excellent prediction performance.