In this paper, we propose MIMO OFDM radar with sufficient cyclic prefix (CP), where all OFDM pulses transmitted from different transmitters share the same frequency band and are orthogonal to each other for every subcarrier in the discrete frequency domain. The orthogonality is not affected by time delays from transmitters. Thus, our proposed MIMO OFDM radar has the same range resolution as single transmitter radar and achieves full spatial diversity. Orthogonal designs are used to achieve this orthogonality across the transmitters, with which it is only needed to design OFDM pulses for the first transmitter. We also propose a joint pulse compression and pulse coherent integration for range reconstruction. In order to achieve the optimal SNR for the range reconstruction, we apply the paraunitary filterbank theory to design the OFDM pulses. We then propose a modified iterative clipping and filtering (MICF) algorithm for the designs of OFDM pulses jointly, when other important factors, such as peak-to-average power ratio (PAPR) in time domain, are also considered. With our proposed MIMO OFDM radar, there is no interference for the range reconstruction not only across the transmitters but also across the range cells in a swath called inter-range-cell interference (IRCI) free that is similar to our previously proposed CP based OFDM radar for single transmitter. Simulations are presented to illustrate our proposed theory and show that the CP based MIMO OFDM radar outperforms the existing frequency-band shared MIMO radar with polyphase codes and also frequency division MIMO radar.