We have investigated the ultrafast carrier dynamics of ZnO/ZnMgO quantum wells by the time resolved measurement using the femtoscond Ti:sapphire oscillator from above band gap to band tail (358-385 nm). As the photo-excited energy above the band gap of the ZnO, the effect of the band filling (BF) and band gap renormalization (BGR) will occur sequentially and compete to each other. As excited photon energy within below band-gap and near exciton resonance, only positive transmission change can be seen that is due to band filling. The maximum transmission change will occur at the free exciton resonance and reveal the saturation behavior at higher exited intensity. In our estimation, exciton binding energy about 76 meV is obtained by the difference between the band gap and exciton resonance that is larger than the ZnO due to quantum confinement effect. In comparing with the ZnO thin films, the exciton dynamics of MQW have a longer radiation time (200ps) that can be explained by quantum confined stark effect (QCSE) by internal field in the hetero-structure. When we increase pumping density near exciton state, screening of QCSE will result in reduction of spontaneous emission lifetime. At shallow band tail states, both BF and BGR effects will exist after excitation of carriers that is similar to that at far above band gap. In our measurement, the two-photon absorption (TPA) is observed and the maximum value is located at excited state of 376 nm. Deep band tail has weak absorption and slow decay might due to phonon-assisted transferring to deeper states.