The improved quark mass density- dependent model, which has been successfully used to describe the properties of both finite nuclei and bulk nuclear matter, is extended to include the strange quark. The parameters of the model are determined by the saturation properties of bulk matter. Then the given parameter set is employed to investigate both the properties of strange hadronic matter and those of $Lambda$ hypernuclei. Bulk strange hadronic matter consisting of nucleons, $Lambda$- hyperons and $Xi$- hyperons is studied under mean-field approximation. Among others, density dependence of the effective baryon mass, saturation properties and stability of the physical system are discussed. For single-$Lambda$ hypernuclei, single particle energies of $Lambda$ hyperon is evaluated. In particular, it is found that the present model produces a small spin-orbit interaction, which is in agreement with the experimental observations. The above results show that the present model can consistently describe the properties of strange hadronic matter, as well as those of single $Lambda$ hypernuclei within an uniform parameterization.
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