We investigate a two-photon ionization process in a real hydrogen atom by short and intense chirped laser pulses. Our simulation of the laser-atom interaction consists on numerically solving the three-dimensional time-dependent Schrodinger equation with a spectral method. The unperturbed wave functions and electronic energies of the atomic system were found by using an accurate L² discretisation technique based on the expansion of the wave functions on B-spline functions. We show the efficiency of chirped laser pulses to control the ionization yield and the transfer of the population to the 2p bound state involved in the ionization path.