The location-based services can provide users with the requested location information. But users also need to disclose their current location to the location-based service provider. Therefore, how to protect user's location privacy is a major concern. In this paper, we propose a heterogeneous deniable authenticated encryption scheme called HDAE for location-based services. The proposed scheme permits a sender in a public key infrastructure environment to transmit a message to a receiver in an identity-based environment. Our design utilizes a hybrid encryption method combing the tag-key encapsulation mechanism (tag-KEM) and the data encapsulation mechanism (DEM), which is well adopted for location-based services applications. We give how to design an HDAE scheme utilizing a heterogeneous deniable authenticated tag-KEM (HDATK) and a DEM. We also construct an HDATK scheme and provide security proof in the random oracle model. Comprehensive analysis shows that our scheme is efficient and secure. In addition, we give an application of the HDAE to a location-based services system.