The potential for probing the impacts of the left-right symmetric model(LRM) on the process e+e- → μ+μ-at a proposed Z0-factory is investigated. Under different electron-positron polarization collision modes, we calculate and compare the deviations of various observables in the framework of the LRM from the standard model(SM)predictions, such as the total cross section, the distribution of the transverse momentum ofμ-, and the forward-backward charge asymmetry ofμ-. In addition, we present the relations between the observables and the LRM parameters. We conclude that it is possible to observe the effects of the LRM on the process e+e- → μ+μ-by using optimal observables and favorable parameters at a Z0-factory.