In this paper, we propose a novel scheme termed layered orthogonal frequency division multiplexing with index modulation (L-OFDM-IM) to increase the spectral efficiency (SE) of OFDM-IM systems. In L-OFDM-IM, all subcarriers are first divided into multiple layers, each determining the active subcarriers and their modulated symbols. The index modulation (IM) bits are carried on the indices of the active subcarriers of all layers, which are overlapped and distinguishable with different signal constellations so that the number of the IM bits is larger than that in traditional OFDM-IM. A low-complexity detection is proposed to alleviate the high burden of the optimal maximum-likelihood detection at the receiver side. A closed-form upper bound on the bit error rate, the achievable rate, and diversity order are derived to characterize the performance of L-OFDM-IM. To enhance the diversity performance of L-OFDM-IM, we further propose coordinate interleaving L-OFDM-IM (CI-L-OFDM-IM), which interleaves the real and imaginary parts of the modulated symbols over two different subchannels. Computer simulations verify the theoretical analysis, and results show that L-OFDM-IM outperforms the conventional OFDM-IM scheme. Moreover, it is also confirmed that CI-L-OFDM-IM obtains an additional diversity order in comparison with L-OFDM-IM.