The magnetohydrodynamic axisymmetric instability of a streaming gas jet surrounded by bounded fluid with non-uniform field has been developed. The problem is formulated, solved and the boundary conditions are applied across the interfaces. The eigenvalue relation is derived and discussed analytically and the results are confirmed numerically. Some reported works are recovered as limiting cases from the present general results. The streaming has a destabilizing effect for all short and long wavelengths. The capillary force is stabilizing for short wavelengths but it is destabilizing for long wavelengths. The axial magnetic fields interior the gas and fluid media are stabilizing. The transverse field is destabilizing for all wavelengths. The radii ratio of the gas and fluid cylinders plays an important role for stabilizing the model and made it more realistic one than the full liquid jet or/and the ordinary hollow jet. The numerical analysis clarify the stable and unstable domains based on different values of the various parameters of the problem.