In this paper, the use of index modulation (IM) technique for non-orthogonal multiple access (NOMA) is presented, called the Index Modulation multiple access (IMMA). From the concept of index modulation, IMMA technique uses the active subcarriers and inactive subcarriers to make index indices. The index indices can carry bits in addition to the QAM modulation bits, which enables IMMA to have better energy efficiency (EE). Also, IMMA can choose the active and inactive subcarrier combinations to achieve different spectral efficiency (SE) and energy efficiency (EE) for flexibility. In IMMA, each user chooses the active codeword according to the index bits, and shares the same time-frequency resources to do multiple access. By combining index modulation and multiple access, IMMA can improve the SE and EE relative to other multiple access schemes. The SE and EE between different multiple access schemes are compared. Moreover, the IMMA average bit error rate (ABER) performance using maximum likelihood (ML) detection and the ABER error bound are devised. Our simulation results show that IMMA always has better EE than orthogonal frequency division multiple access (OFDMA). Better SE can also be achieved. Furthermore, IMMA always has better SE and EE relative to sparse code multiple access (SCMA).