The metal prices play an important role in many aspects of economics. Copper, a widely used metal in the industry, has received an extensive attention recently. Due to the high fluctuations in copper price that makes it difficult to predict especially when using the traditional statistical models, in this work, a hybrid Neural Network with Bayesian Optimization and Wavelet Transform is applied to forecast the copper price in both short- and long-terms, in which Bayesian Optimization Algorithm is used on the hyperparameter searching task, the Wavelet Transform is applied to denoise the data and eliminate the irrelevant information, and Long Short Time Memory (LSTM) and Gated Recurrent Units (GRU) are employed to train the data and predict future copper price, respectively. The results indicate that our methods, either LSTM or GRU, can appropriately predict the copper price for both short- and long-terms with mean squared error both below 3% and this hybrid Neural Network is robust to remove the irrelevant information and search the optimized set of hyperparameters. Meanwhile, it is easily and readily applicable to predict the prices of other commodities (i.e., stock market).