  We calculated the masses of neutral and charged pion and pion decay constants
under an extra magnetic field at zero temperature. The quantum fluctuations are
integrated through the functional renormalization group. We consider the quark
and meson propagators in the Landau level representation and weak-field
expansion, respectively. The neutral pion mass monotonically decreases with the
magnetic field, while the charged pion mass monotonically increases with the
magnetic field. The pion decay constant and the quark mass show the magnetic
catalysis behavior at vanishing temperature. The neutral pion mass and pion
decay constant are quantitatively in agreement with the lattice QCD results in
the region of $eB < 1.2 {\rm GeV}^2$, and no non-monotonic mass behavior for
charged pion has been observed in this framework.
