Nowadays, many applications, like Internet of Things and Industrial Internet, collect data points from sensors continuously to form long time series. Finding correlation between time series is a fundamental task for many time series mining problems. However, most existing works in this area are either limited in the type of detected relations, like only the linear correlations, or not handling the complex temporal relations, like not considering the unaligned windows or variable window lengths. In this paper, we propose an efficient approach, Non-Linear Correlation search (NLC), to search the correlated window pairs on two long time series. Firstly, we propose two strategies, window shrinking and window extending, to quickly find the high-quality candidates of correlated window pairs. Then, we refine the candidates by a nested one-dimensional search approach. We conduct a systematic empirical study to verify the efficiency and effectiveness of our approach over both synthetic and real-world datasets.