In this paper, we introduce a construction of 16-QAM sequences based on known binary sequences using multiple sequences, interleaved sequences and Gray mappings. Five kinds of binary sequences of period N are put into the construction to get five kinds of new 16-QAM sequences of period 4N. These resultant sequences have 5-level autocorrelation {0, ±8, ±8N}, where ±8N happens only once each. The distributions of the periodic autocorrelation are also given. These will provide more choices for many applications.