A very simple and highly accurate method of investigating the behavior of atomic system in a strong magnetic field has been developed based on the generalized pseudospectral discretization. As examples, we present the calculations of the binding energies and quadruple moments for the ground and low-lying excited states of the hydrogen atom in a magnetic field ranging from zero up to 1000 a.u.. The obtained results are found to be in excellent agreement with other high-accuracy theoretical calculations. The present method may be straightforwardly applied to cross electric-magnetic field in an arbitrary orientation.