As a basic model to describe strongly correlated Bose gases in lattice potential, the Bose-Hubbard model has been a hot topic in physics since it was proposed. The extension of the Bose-Hubbard model to a two-component coupled gas is straightforward and interesting. In particular, when the two components of bose gas experience completely different lattice potentials and interactions, the system will show very different properties from that of a single-component gas. Similarly, the interactions between itinerant and local particles in heavy fermion systems have been extensively studied, and a wealth of quantum phenomena have been discovered. So, what kind of novel phenomena will be produced by itinerant particles and local particles in the bosonic quantum system? In this paper, we consider the ground state properties of a two-component lattice boson system assisted by an optical cavity. In the vacuum environment, we assume that the two components of the bose gas are trapped in an optical lattice dependent on the spin internal states, where one component is completely local and the other is itinerant, and cavity photons can induce tunneling between the two components.In this work, variational method and self-consistent mean field approach are used to study the ground state properties of the system. These two methods have their own applicable scope and analytical advantages. In the case of the hard-core limit, the Hilbert space of the system is greatly reduced, and the analytical expression of the energy density of the system can be easily obtained by using the variational wave function, and the ground state properties of the system can be obtained by solving each parameter of the system through analytic calculation. However, in any real experimental system, the interactions between atoms are always finite, and the Hilbert space of the system is no longer restricted. In principle, the self-consistent mean field approach can deal with systems with arbitrary finite interaction strength. Utilizing the mean field decoupling approximation, we can study the quantum phase of the system by simply calculating the order parameters. By comparing the results of the two approaches, we can con-firm the reliability of the calculated results. Therefore, we divide this paper into two cases to fully study the ground state properties of the system, they are the hard-core limit case (the interaction is infinite) and the case where the interaction is finite, respectively.Utilizing the above two approaches, we systematically analyze the ground state properties of the system, and obtain the phase diagrams of the system in different parameter Spaces. The phase diagrams exhibit a wealth of quantum phases, including the Mott insulator phase, the superfluid phase, and the superradiant superfluid phase. We find that, with the help of cavity photons, the bosons of itinerant component can induce the quantum phase transition of the localized component from a Mott insulating phase to a superfluid phase. When the coupling strength of light and atom is nonzero, the average particle number per lattice site is closely related to specific quantum phases. In particular, the inter-component interaction may induce anomalous quantum phase transition between the Mott insulating and superradiant-superfluid phases in certain parameter regime. Finally, we provide a possible experiment implementation of our model. Our work enriches the physics of the Bose-Hubbard model and provides an instructive guidance for simulating condensed matter phenomena with ultracold atoms inside optical cavity.