This paper is mainly concerned with the global existence and asymptotic behaviour of classical solutions to the three-dimensional (3D) incompressible non-resistive viscous magnetohydrodynamic (MHD) equations with large initial perturbations in a 3D periodic domain (in Lagrangian coordinates). Motivated by the approximate theory of the ideal MHD equations, the Diophantine condition and the magnetic inhibition mechanism in the version of Lagrangian coordinates analyzed, we prove the global existence of a unique classical solution with some class of large initial perturbations, where the intensity of impressed magnetic fields depends increasingly on the $H^{17}\times H^{21}$-norm of the initial velocity and magnetic field perturbations. Our result not only mathematically verifies that a strong impressed magnetic field can prevent the singularity formation of classical solutions with large initial data in the viscous MHD case, but also provides a starting point for the existence theory of large perturbation solutions to the 3D non-resistive viscous MHD equations. In addition, we also show that for large time or sufficiently strong impressed magnetic fields, the MHD equations converge to the corresponding linearized pressureless equations in the algebraic convergence-rates with respect to both time and field intensity.