For hydrogen atom imbedded in Debye plasmas with an external magnetic field, the combined effect on bound-bound transitions has been investigated. The electron eigenenergies and wave functions are determined by non-perturbatively solving the Schrdinger equation. Both transition frequencies and oscillator strengths are presented for a wide range of plasma screening parameters and external magnetic field strengths. With increasing the plasma screening, the shielding effects on the Lyman series are shown to be decreased in its intensity and the red-shift of its frequency. After adding an external magnetic field, atomic energy levels undergo even stronger perturbation, and the line shapes become polarized. The non-perturbative effect is significant for the quantum states (n 3). Comparisons made with other theoretical calculations are shown in good agreement. The results reported here may be useful for the interpretation of spectral properties of H-like ions in laboratory and astrophysical Debye plasmas.