This letter presents a novel unipolar scheme called X-transform optical orthogonal frequency division multiplexing with index modulation (XO-OFDM-IM) for underwater optical wireless communication (UOWC). Unlike the conventional schemes, each modulated data in XO-OFDM-IM is transmitted via one or two subcarriers; and the information bits carried by the index of subcarriers are used to produce positive and real time-domain signal without the need for adding direct current (DC) bias or clipping processes. The performance of the proposed scheme has been evaluated via a 2-meter measured UOWC channel to validate its outperformance against its benchmarks. For instance, our scheme offers up to 7 dB improvement in term of signal to noise ratio at a target bit error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> and up to 8 dB in term of peak-to-average power ratio (PAPR) compared to its counterpart asymmetrically clipped O-OFDM (ACO-OFDM) when considering the same spectral efficiency (SE).