This paper investigates the axisymmetric and the first non-axisymmetric linear instability of a charged viscoelastic jet under an applied axial magnetic field. The Oldroyd-B model is employed to account for the viscoelastic effect. Viscoelastic fluid is considered to be a leaky dielectric, and the surrounding inviscid gas a perfect dielectric. Results suggest that increasing the axial magnetic field suppresses both the axisymmetric and non-axisymmetric instabilities, and moves the main unstable range of the non-axisymmetric instability to small wavenumber regions. The magnetic field is coupled with the electric field by increasing the critical electric intensity of the dual effects on the axisymmetric mode; it also favors the transition from axisymmetric mode (jetting-dripping motion) to non-axisymmetric mode (jetting-whipping motion). It is also discovered that the magnetic field weakens the effects of fluid elasticity and deformation retardation time, but has little influence on the role played by the ambient gas. (C) 2017 Published by Elsevier B.V.