Compared with standard cyclic prefix OFDM (CP-OFDM), time domain synchronous OFDM (TDS-OFDM) can achieve a higher spectrum efficiency by using the known training sequence instead of CP as the guard interval. However, TDS-OFDM suffers from reduced energy efficiency and performance loss due to the existing mutual inferences. In this paper, based on the newly emerging theory of structured compressive sensing (SCS), we propose a reliable and energy-efficient TDS-OFDM transmission scheme with reduced guard interval power (which is impossible for CP-OFDM) by designing a channel estimation scheme with high accuracy. The wireless channel properties including channel sparsity and inter-channel correlation, which are usually not considered in conventional OFDM schemes, have been exploited. We further exploit the worst-case system design principle to extract multiple interference-free regions of small size to simultaneously reconstruct multiple channels of large size without iterative interference cancellation. In this way, the guard interval power in TDS-OFDM can be reduced to achieve a 20% higher energy efficiency than standard CP-OFDM, and the system reliability can be also improved in fast fading channels.