In this paper, we study the features of the electric current under conditions of the tunnel effect in fractal structures. Based on the electron dispersion law for fractal objects, an expression for finding the tunneling current is obtained. Current-voltage characteristics are constructed for the following contacts: fractalfractal, fractal-metal, fractal-superlattice. The influence of the fractal dimension on the characteristics of the tunneling current is revealed. KEYWORDS fractals, fractions, tunneling, current-voltage characteristic.