Nonlinear electrodynamics with two dimensional parameters is studied. The range of electromagnetic fields when principles of causality, unitarity and the classical stability hold are obtained. A singularity of the electric field at the center of charges is absent within our model and there are corrections to the Coulomb law as $r\rightarrow\infty$. The universe inflation takes place in the background of stochastic magnetic fields. The second stage of the universe evolution is the radiation era so that the graceful exit exists. We estimated the spectral index, the tensor-to-scalar ratio, and the running of the spectral index that are in an approximate agreement with the PLANK and WMAP data.