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We generalize the construction method of the family of binary bent sequences introduced by Olsen, Scholtz, and Welch (1982) to obtain a family of generalized binary bent sequences with optimal correlation and balance property by using the modified trace transform. Then, the conventional binary bent sequence becomes a special case of our construction method. Several families of the generalized binary bent sequences are constructed by using the bent functions on the intermediate field. Using some of the generalized binary bent sequences, new families of binary sequences with optimal correlation and balance property can be constructed by the lifting idea similar to No (1988) sequences, which are referred to as binary bent-lifted sequences.