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The properties of strange quark stars are studied within the quasi-particle model.Taking into account chemical equilibrium and charge neutrality,the equation of state (EOS) of(2 + 1)-flavor quark matter is obtained.We illustrate the parameter spaces with constraints from two aspects:one is based on the astronomical results of PSR J0740 + 6620 and GW 170817,and the other is based on the constraints proposed from the theoretical study of a compact star that the EOS must ensure the tidal deformability A1.4 =190+390-120 and support a maximum mass above 1.97 M☉.It is found that neither type of constraints can restrict the parameter space of the quasi-particle model in a reliable region and thus we conclude that the low mass compact star cannot be a strange quark star.