The thermal conductivity of three-dimensional (3D) strongly coupled complex (dusty) plasmas has been calculated through the improved Evan-Gillan nonequilibrium molecular dynamics (NEMD) algorithm. The extensive NEMD simulations are performed to study the performance of the algorithm and compared the results determined for perturbed heat energy current to the results obtained by equilibrium molecular dynamics (EMD) simulations. The calculations show that the present algorithm gives accurate results with fast convergence and small size effects over a wide range of plasma coupling and screening parameters. The present simulation results are in agreement with part of others NEMD and EMD data in the literature with simulation values generally overpredicting the thermal conductivity by 3%–20%, depending on plasma parameters. It is shown that the homogenous perturbed method can be employed to estimate the thermal conductivity and to understand the fundamental behaviors in 3D complex Yukawa liquids.