Following the recent discovery of a bulk photovoltaic effect in the Pb[(Mg1/3Nb2/3)0.68Ti0.32]O3 crystal, we report here more than one order of magnitude improvement of photovoltaicity as well as its poling dependence in the related composition of lead magnesium niobate-lead titanate noted Pb[(Mg1/3Nb2/3)0.7Ti0.30]O3. Photocurrent measurements versus light intensity reveal a fascinating hysteretic charge carriers dynamics clearly demonstrating charge generation, trapping and release processes.