The light-emitting diode (LED) is the major source of nonlinearity in LED communications, and the nonlinearity needs to be effectively modelled and mitigated to avoid the degradation of communication performance. In indoor LED communications, multipath dispersion can lead to inter-symbol interference (ISI) at high data rates. In this paper, we jointly estimate the LED nonlinearity and ISI channel based on an orthogonal polynomial based technique. Then frequency domain equalization and post-distortion are adopted to mitigate the ISI and nonlinearity. Simulation results are provided to demonstrate the effectiveness of the proposed technique.