Using the variational method based on the Gaussian basis set, the authors investigate the 1u state of hydrogen molecular ion in a non-parallel magnetic field with respect to the fixed molecular axis. At sufficiently small field strength, the equilibrium configuration prefers the perpendicular orientation, in which the (relative) orientation θ between the magnetic field and the molecular axis is 90°. With increasing field strength, the orientation θ of the equilibrium configuration decreases, and is neither the parallel orientation nor the perpendicular orientation at field strength between 10(9) G and 2.35 × 10(10) G. Meanwhile, more and more configurations with large orientations become unstable with respect to the dissociation H + p.