The anisotropic Gaussian basis sets were optimized for the H atom and the hydrogen molecule in strong magnetic fields of 0-1000 a.u. We used five-parameter fit functions to generate anisotropic Gaussian exponents of hydrogenic atomic orbitals. These functions provided errors of energy that were comparable to the independent optimization of all the exponents. The optimal exponents were used to calculate the Hartree-Fock energies of H-2 at arbitrary orientations, with respect to the magnetic field. Furthermore, the double-exponential transformation was applied to calculate highly anisotropic Coulomb integrals. Between magnetic field strengths of 1 a.u. and 100 a.u., a molecule in a triplet ground state continuously changed its stable orientation from the perpendicular geometry to the parallel geometry.