In this paper, the idea of offset spatial modulation (OSM) is integrated with orthogonal frequency division multiplexing (OFDM), toward an efficient design to bridge their advantages. Compared to its conventional counterpart as spatial modulation (SM)-OFDM, the proposed OSM-OFDM scheme aims at providing a simplified implementation structure with less number of radio frequency (RF) chains, by introducing an offset between the RF chain and the index of the activated transmit antenna on each subcarrier. Specifically, three types of offset antenna selection (OAS) methods are developed to meet different scene requirements for different number of available RF chains. Furthermore, through theoretical analysis, we quantify the bit error rate upper bounds of OSM-OFDM with different types of OAS methods. Finally, extensive computer simulations demonstrate that OSM-OFDM provides a flexible tradeoff among implementation cost, computation complexity and error performance.