Band assignment is an important function in multi-band heterogeneous networks. Most of the existing works have considered the rate of user equipment (UE) as a key criterion for the band assignment. However, the power consumption at the mmWave band is significantly higher than the Sub-6 GHz band, which is particularly significant because the UE battery power is limited. In this context, we design a novel long short term memory (LSTM) aided energy efficient band assignment system for a moving UE. Corresponding to the realistic scenario, we apply a timeseries split based approach to train and test the model. The proposed policy is validated on the publicly available ‘DeepMIMO’ dataset. Research findings shows that the RMSE of predicted rate using timeseries split approach is much less than the conventional approach. Moreover, with proposed scheme, the median energy efficiency is 56.30% higher as compared to the case when energy usage is not considered in the bandswitching decision, while the median rate with our proposed scheme reduces only by 13.81%.