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By considering the pseudogap effect, the doping and energy dependences of thermal conductivity in cuprate superconductors are studied. Our results show that the thermal conductivity as a function of energy exhibits a characteristic peak from underdoping to overdoping due to the presence of the pseudogap in pseudogap phase of cuprate superconductors. The thermal conductivity is strongly doping dependent. On the one hand, with increasing doping concentration, the weight of thermal conductivity increases quickly, especially the residual thermal conductivity which is in qualitative agreement with the experimental data. On the other hand, the characteristic energy corresponding to the position of the characteristic peak decreases monotonically upon increasing doping concentration, and it scales with the doping dependence of pseudogap. In particular, we have studied the doping dependence of the ratio of quasiparticle velocities normal and tangential to the Fermi surface at the nodes . It is shown that increases with the increase of doping concentration. Moreover, we explain that both the residual thermal conductivity and increase rapidly upon the increase in doping concentration in heavily overdoped cuprate superconductors. [ABSTRACT FROM AUTHOR]