As one of the 5G candidate technologies, F-OFDM (Filtered-OFDM) inherits the advantages of OFDM(Orthogonal Frequency Division Multiplexing) technology and has outstanding advantages in flexibility and combating system delay, but it still has the problems of frequency offset sensitivity and large peak-to-peak average. To overcome these shortcomings, F-OFDM Index Modulation system is proposed in this paper. Firstly, the system divides the transmission data on each subband of the F-OFDM system into index modulation bits and constellation modulation bits. The index bits are used to select the active subcarriers, and then the constellation modulation symbols are placed on the active subcarriers for transmission. Finally, different detection algorithms， such as ML (Maximum Likelihood) detection or Energy detection are used to demodulate to obtain the estimated transmit symbol at the receiver. The analysis and simulation results show that the system can not only effectively suppress the influence of frequency offset on system performance, but also reduce the high peak-to-average ratio of F-OFDM system, which has certain practical research significance.