Underwater acoustic communications (UAC) channels are well known to be bandlimited due to the low acoustic carrier frequency. In terrestrial communications, multi-input multi-output (MIMO) schemes have long been proved to provide improved capacity without bandwidth expansion. However, the application of these MIMO designs, especially coherent ones, is challenging since UAC channels are spreading in both the time delay domain and the frequency domain. In such extremely bandlimited and doubly-selective channel conditions, the pilots necessary for accurate channel estimation can considerably reduce the bahndwidth efficiency of the system. To avoid such problems, we propose a differential MIMO scheme for doubly-selective UAC channels. Our approach is based on orthogonal space-time block coding (OSTBC), but bypasses channel estimation. As a result, not only a higher bandwidth efficiency is preserved, but also the processing complexity at the receiver is reduced. We adopt the basis expansion model (BEM) to model the doubly-selective channels. Both analytical and numerical results show that our approach can collect full 3-dimensional diversity: space, Doppler and multipath. The results are verified over both the generated channels using Jakes' model and the estimated channels from a real underwater experiment.