Orthogonal frequency division multiplexing with index modulation (OFDM-IM) is a recently developed technique which modulates part of the information bits using the indices of OFDM subcarriers. In this letter, a simple and efficient subcarrier-level interleaving scheme is introduced to improve the performance of conventional OFDM-IM through enlarging the Euclidean distances among the modulated symbols. Both theoretical analysis and simulation results are presented to show that the proposed OFDM with interleaved sucarrier-index modulation (OFDM-ISIM) can achieve better system performance than conventional OFDM-IM and OFDM with low-order modulation schemes such as binary phase shift keying, quadrature phase shift keying and 16 quadrature amplitude modulation.