The OFDM technology is widely used in wireless communication systems, but it is highly sensitive to narrowband interference (NBI). The existing NBI suppression algorithms are mainly for single NBI or multiple NBIs with an assumption that the frequency distance of the multiple NBIs is large enough. However, in reality, there are more and more multiple interacting NBIs with small frequency distance, such as NB-IoT. Unfortunately, due to the interaction of multiple NBIs, the performance of existing NBI suppression algorithms is degraded. Aiming at this problem, we propose a multiple interacting NBIs suppression algorithm jointed time-frequency domain for OFDM systems. First, in order to achieve a high-precision and low-complexity frequency estimate for a single NBI, an interference frequency estimation method based on chirp-z transform (CZT-IFE) is studied. Then, for multiple interacting NBIs, based on the analysis of NBI frequency distance and spectral aliasing, a highly robust interference frequency estimation method combining IIR notch filter and CZT-IFE (NF-CZT-IFE) is given. It eliminates the interaction of multiple NBIs and obtains the accurate frequency estimates of the NBIs. Finally, based on NF-CZT-IFE, the multiple interacting NBIs are suppressed by using IIR notch filters. Simulation results demonstrate that the proposed multiple interacting NBIs suppression algorithm has better interference suppression performance on the NBIs with different frequency distances and different interference numbers. The proposed algorithm improves the robustness of OFDM systems in complex NBI environments.