We describe a theoretical method, developed in the coupled-channel formalism, to study photoionization of H atoms in a strong magnetic field of a size that is typical for magnetic white dwarfs. The coupled Schrödinger equations are solved numerically using the renormalized Numerov method proposed by Johnson [B. R. Johnson, J. Chem. Phys. 67, 4086 (1977)10.1063/1.435384; B. R. Johnson, J. Chem. Phys. 69, 4678 (1978)10.1063/1.436421]. The distinct advantage of this method is the fact that no overflow problems are encountered in the classically forbidden region, and hence the method exhibits excellent numerical stability. Photoionization cross sections are presented for magnetized H atoms in the ground and 2p excited states. The calculated results are compared with those obtained by other theories. The present method is particularly useful for explaining the complex features of continuous spectra in a strong magnetic field and hence provides an efficient tool for modeling photoionization spectra observed in the atmosphere of magnetic white dwarfs.