  We consider running coupling constant in holographic model with external
magnetic field supported by Einstein-dilaton-three-Maxwell action. We obtain a
significant dependence of the running coupling constant $\alpha$ on chemical
potential, temperature and magnetic field. We use the boundary condition that
ensures the agreement with lattice calculations of string tension between
quarks at zero chemical potential. The location of the 1-st order phase
transitions in $(\mu, T)$-plane does not depend on the dilaton boundary
conditions. We observe that running coupling $\alpha$ decreases with increasing
magnetic field for the fixed values of chemical potential and temperature. At
the 1-st order phase transitions the functions $\alpha$ undergo jumps depending
on temperature, chemical potential and magnetic field.
