Abstract: A fractal resistor network is constructed by infinite iterations of midpoint triangle or titled regular triangles whose sides are replaced by resistance wire. The distribution and scale coefficients of currents on some nodes are invariant by the self-similarity conditions. These coefficients are calculated from the Kirchhoff law. Also，the equivalent resistance between two nodes are derived by the line relationship of resistor network.

Key words: triangle, fractal network, distribution coefficient of current, equivalent resistance