We present a new method to calculate photoionization spectra which originate in the interaction of a molecule with ultrashort strong laser pulses of arbitrary time and frequency shapes. Concepts of the multiconfiguration time-dependent Hartree method, initially developed for the propagation of multidimensional wave packets are combined with the fast-Fourier-transform split-operator method. The presented method allows for a fast and stable nonperturbative description of multiphoton excitation and ionization processes in small molecules. As an example we calculate the kinetic energy distribution of photoelectrons from intense short pulse ionization of Na-2.