By employing a nanosecond pump-probe method, biexciton formation process was investigated in ZnO/Zn1-xMgxO (x=0.26) multiple quantum wells (MQWs) grown on ScAlMgO4 substrate by laser molecular-beam epitaxy. Bleaching of absorption due to the saturation of excitonic states, and induced absorption related to the exciton-biexciton transition were observed in their spectra. It is demonstrated that the pump-probe method allows us to precisely determine binding energies of exciton complexes even applied to the semiconductor quantum structures where the localization effect are not negligible. This is because a transition from free-excitonic states to free-biexcitonic states is involved in the induced absorption process. The biexciton binding energy is a monotonically decreasing function of well width (L-w). For the MQWs with L-w smaller than 2.5 nm, the biexciton binding energy is larger than 25 meV, comparable to the thermal energy of room temperature.