A general construction of binary interleaved sequences of period 4N with low autocorrelation are considered in the paper. Firstly, some correlation properties of two general classes of binary interleaved sequences are presented. Secondly, based on these results, autocorrelation functions of a general construction of binary interleaved sequences of period 4N are given. Finally, we show that, from these results for general cases, several known binary sequences of these types with optimal autocorrelation and some other new binary sequences with low autocorrelation can be constructed.