Nowadays, a basic commodity for a human being to lead a standard lifestyle with human comfort irrespective of the nature of environmental conditions is electric power. The electricity load demand increases tremendously especially for a metropolitan city due to climatic conditions, population growth, local area development, industries expansion, air pollution, thermal device usage, etc. Hence, the accuracy of electricity load and its price forecasting is a deciding factor for the power distribution network to retain as an efficient, sustainable, and secure consumer-friendly network. On the other hand, based on the volatile, intermittent, and uncertain behavior of electricity load and price, an accurate, and robust forecast model should be designed. In this paper, a new hybrid forecast model for short-term electricity load and price prediction has been developed. The proposed method includes three modules: wavelet transform that is used to eliminate fluctuation behaviors of the electricity load and price time series, feature selection based on entropy and mutual information has been proposed to rank candidate inputs and eliminate redundant inputs according to their information value, and a new learning algorithm. The proposed learning method consists of a deep learning algorithm with LSTM networks which improves the accuracy of predictions. The performance of the proposed method has been validated successfully on load and price data collected from the Pennsylvania-New Jersey-Maryland (PJM) and Spain electricity markets. Also, for further test, the load data in Iran have been used.