  We study electromagnetic field effect on charmonium gluon-dissociation in
quark-gluon plasma. With the effective Hamiltonian derived from QCD multipole
expansion under an external electromagnetic field, we first solve the two-body
Schr\"odinger equation for a pair of charm quarks with mean field potentials
for color and electromagnetic interactions and obtain the charmonium binding
energies and wave functions, and then calculate the gluon-dissociation
cross-section and decay width by taking the color electric and magnetic dipole
interactions as perturbations above the mean field and employing Fermi's Golden
Rule. Considering the charmonium deformation in magnetic field, the discrete
Landau energy levels make the dissociation cross-section grow hair, and the
electric dipole channel is significantly changed, especially for the $P-$wave
states $\chi_{c0}$ and $\chi_{c\pm}$. From our numerical calculation, the
magnetic field strength $eB=5~m_\pi^2$ already changes the gluon dissociation
strongly, which may indicate measurable effects in high-energy nuclear
collisions.
