Geo-Indistinguishability (GI) is a powerful privacy model that can effectively protect location information by limiting the ability of an attacker to infer a user's true location. In real life, locations usually have different sensitive levels in terms of privacy; for example, shopping malls might be low-sensitive while home addresses might be high-sensitive for users. But the GI model does not consider the various sensitive levels of locations, and implements the same perturbation on all locations to meet the highest privacy requirement. This would cause overprotection of low-sensitive locations and reduce data utility. To strike a good balance between privacy and utility, in this paper, we propose a novel privacy notion, termedLocation-DiscriminativeGeo-Indistinguishability (LDGI), which takes into account different sensitive levels of location privacy. With LDGI model, we then develop a perturbation scheme called EM-LDGI based on the exponential mechanism, and an advance scheme MinQL to further enhance data utility. To improve the efficiency of the proposed schemes, we design a scheme MinQL-S with the assistance of the spanner graph, at the cost of a slight utility degradation. We theoretically analyze that the proposed schemes satisfy LDGI and evaluate their performance by extensive experiments on both synthetic and real datasets. The comparison with GI mechanisms demonstrates the advantages of the LDGI model.