To supplement missing logging information without increasing economic cost, a machine learning method to generate synthetic well logs from the existing log data was presented, and the experimental verification and application effect analysis were carried out. Since the traditional Fully Connected Neural Network (FCNN) is incapable of preserving spatial dependency, the Long Short-Term Memory (LSTM) network, which is a kind of Recurrent Neural Network (RNN), was utilized to establish a method for log reconstruction. By this method, synthetic logs can be generated from series of input log data with consideration of variation trend and context information with depth. Besides, a cascaded LSTM was proposed by combining the standard LSTM with a cascade system. Testing through real well log data shows that: the results from the LSTM are of higher accuracy than the traditional FCNN; the cascaded LSTM is more suitable for the problem with multiple series data; the machine learning method proposed provides an accurate and cost effective way for synthetic well log generation.