In this work, a lattice Boltzmann flux solver (LBFS) is presented for simulation of conjugate heat transfer problems. Specifically, the mass and momentum equations used in the flow domain and the energy equation applied in both the flow and solid domains are discretized by finite volume method (FVM) and the numerical fluxes at the cell interface are reconstructed by the local solution of lattice Boltzmann equation (LBE) truncated to the Navier-Stokes level. To calculate the numerical fluxes, the Chapman-Enskog analysis is carried out first to reveal the connection between the macroscopic fluxes and the solution of LBE. With this relationship, the macroscopic fluxes can then be calculated locally and independently at each cell interface by the solution of LBE, which makes the developed scheme be very easy for application on non-uniform mesh and curved boundary as compared with lattice Boltzmann method (LBM). Overall, the present method well combines the advantages of simplicity and kinetic nature of LBM and geometric flexibility of Navier-Stokes solver discretized by FVM. In addition, in the calculation of numerical flux of energy equation, the concept of thermal resistance is innovatively introduced to evaluate the thermal conductivity at the cell interface. As compared with simple average technique, the introduced strategy can provide a more accurate prediction for temperature field. Numerical results showed that the solid-solid and fluid-solid conjugate heat transfer problems can be well simulated by the developed scheme and the second-order accuracy is achieved in space. (C) 2019 Elsevier Ltd. All rights reserved.