The melting and solidification of phase change material (PCM) in a horizontal eccentric shell-and-tube latent heat storage (LHS) unit were numerically studied to design a high-efficiency LHS configuration. Firstly, the melting and solidification in a concentric configuration were studied to reveal the influence of natural convection. The results show that, because of natural convection, the solid PCM above the tube has a high melting rate during the melting process and the liquid PCM under the tube has a high solidification rate during the solidification process. Then the eccentric tube configuration was used to take the best advantage of natural convection. The results show that the eccentric tube with the tube moving to the downside can efficiently enhance the PCM melting rate. The best melting performance can be obtained when the eccentricity (ε) is -0.6, where the PCM melting time reduces about 29.8% compared with the concentric tube. However, the downward movement of the tube seriously weakens the PCM solidification rate and causes total performance deterioration of the entire melting and solidification cycle. For the whole melting and solidification cycle without rotation, the minimum total time is obtained at ε= 0.1 which is only 1.3% less than the total time at ε= 0. A new LHS unit with a rotation configuration was proposed to enhance PCM melting and solidification rates simultaneously. The validation results show the optimum heat transfer performance for the whole melting and solidification cycle can be obtained when ε = -0.2, where the total melting and solidification time reduces by 11.1% compared with concentric configuration.