In this letter, we present a novel non-quasi-2D slow-wave structure (NQSWS) for THz sheet beam traveling-wave tubes (THz SB TWTs), which have been conceived, fabricated and tested. Our proposed structure differs from the conventional quasi-2D structure, in which featured cosine fluctuation in the horizontal direction on the metallic roof in the proximity of the SB tunnel. This modification results in lower cutoff frequency, flatter dispersion property, and higher average interaction impedance. Comparing with its quasi-2D counterpart with the same tunnel area, the two-section NQSWS-TWT reaches a maximum power of 285 W (32% increase) at 220 GHz, while achieving 3-dB bandwidth of 17 GHz (13% increase), according to particle-in-cell simulations. Additionally, the NQSWS can significantly reduce the magnetic field (10% reduction) while guaranteeing full beam transmission. Finally, the cold test demonstrates good consistency with the theoretical simulations, which confirms its feasibility as novel SWS in the THz TWTs applications.