We consider a single quantum mechanical particle confined to an one-dimensional (1D) infinite square well, and propose a nonequilibrium quantum Otto cycle (NQOC). Compared with the conventional quantum Otto engine (CQOE) investigated by [T.D. Kieu, Phys. Rev. Lett. 93, 140403 (2004); T.D. Kieu, Eur. Phys. J. D 39, 115 (2006)], due to the effects of negentropy produced in the NQOC, many interesting features appear: (1) in general, the NQOC is capable of extracting more work, so it is more efficient; (2) the NQOC can operate even when T 1 = T 2 or T 1 < T 2, where T 1 (T 2) represents the temperature of hot (cold) bath; (3) in some cases, the NQOC can absorb heat from both baths and completely transforms them into work. These results demonstrate that the negentropy can be understood as an effective source of efficiency in quantum heat engines (QHEs) and meanwhile it is shown that the second law of thermodynamics is not violated. At last, we also show that the efficiency of NQOC reduces to that of classical Otto cycle in the classical limit.