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Heat conduction of symmetric Frenkel-Kontorova(FK)lattices with a coupling displacement was investigated in the overdamped case and underdamped case respectively.In the overdamped case,the results indicate that:(i)As the coupling displacement equals to zero,temperature oscillations of the heat baths linked with the lattices can control magnitude and direction of the thermal current;(ii)Whether there is a temperature bias or not,the thermal current oscillates periodically with the coupling displacement,whose amplitudes become greater and greater;(iii)As the coupling displacement is not equal to zero,the thermal current monotonically both increases and decreases with temperature oscillation amplitude of the heat baths,depending on values of the coupling displacement;(iv)The coupling displacement also induces non-monotonic behaviors of the thermal current with respect to spring constant of the lattice and coupling strength of the lattices;(v) These dynamical behaviors comes from the interaction of the coupling displacement with periodic potential of the FK lattices.In the underdamped case,the results indicate that:(i)As the system has less atoms and is symmetric,the coupling displacement can boost up its thermal current,and absolute value of the thermal current as a function of the coupling displacement exhibits one or two peaks,determined by period of the FK lattices.(ii)As the system has less atoms and is asymmetric,the coupling displacement affects its thermal current only in the case of either negative temperature difference or positive temperature difference,depending on asymmetry of the on-site potentials of the FK lattices.(iii)Along with an increasing atomic number of the FK lattices,the effect of the coupling displacement on the system gradually disappears.Our results have the implication that the coupling displacement between nonlinear lattices plays a crucial role in the design of thermal devices.