For fast-moving vehicles, radio channels can be severely fast-fading. Under such circumstances, the performance of multi-carrier communication systems, such as OFDM-based ones, are often limited by the inter-carrier interference (ICI) caused by time variation of the channel within one transmit symbol. The conventional way to mitigate the effect of ICI is to increase the frequency spacing between neighboring sub-carriers; yet it leads to the decrease of spectral efficiency. Many types of ICI cancellation methods have been developed. Most of them are only effective for mild to medium ICI, and the ones that are effective for severe ICI either suffer from heavy computational cost or need transmitter-side modifications and thus may not be standard compatible. In this paper, we report a maximum a posteriori (MAP) ICI equalizer that are effective for severe ICI and with acceptable computational cost. Two advantages make it stand out as a very promising technical choice. First, it utilizes an ICI indicator that we introduced in [1] and [2] to build a variable-width trellis such that the computational cost can be dramatically reduced. Second, it is possible to loop the MAP equalizer and an outer channel decoder to form an iterative receiver to further enhance the system performance. This receiver-side technique can improve the reliability of communication systems under high mobility or increase spectral efficiency under mild to medium mobility.