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In this study, the authors propose a new concept named similar-bent function and the authors present two general methods to construct balanced sequences with low correlation by using similar-bent functions and orthogonal similar-bent functions. The authors find that the bent sequence sets are special cases of our construction. The authors also investigate the linear complexity of the new constructed sequences. If a suitable similar-bent function is given, the sequences constructed by it can have high-linear complexity. As examples, the authors construct two new low-correlation sequence sets. One constructed based on Dobbertin's iterative function is asymptotically optimal with respect to the Welch bound and the other one is constructed based on Kasami function whose sequences have a high-linear complexity.