A method to characterize attosecond extreme ultra violet (XUV) pulses from photoelectron spectra of atoms is presented. A pump pulse prepares a coherent superposition of two atomic bound states, from which photoionization takes place after variable time delays by the attosecond XUV pulse. Information on the spectral phase of the attosecond XUV pulse is extracted from the analysis of photoelectron spectra as a function of photoelectron energy and time delay. Together with information on the spectral intensity obtained from a separate optical measurement, a temporal shape of the attosecond XUV pulse can be precisely reconstructed. After the theoretical formulation of the problem, we present numerical examples for H atom and show that, depending on the choice of energy separation of two bound states, a different accuracy is reached to characterize attosecond XUV pulses.