N-continuous orthogonal frequency division multiplexing (NC-OFDM) was demonstrated to provide significant sidelobe suppression for baseband OFDM signals. However, it will introduce severe interference to the transmit signals. Hence in this letter, we specifically design a class of low-interference NC-OFDM schemes for alleviating the introduced interference. Meanwhile, we also obtain an asymptotic spectrum analysis by a closed-form expression. It is shown that the proposed scheme is capable of reducing the interference to a negligible level, and hence to save the high complexity of signal recovery at the receiver, while maintaining similar sidelobe suppression performance compared to traditional NC-OFDM.