The time-varying (TV) chaos unitary matrix based differential multiple-input multiple-output (D-MIMO) system is capable of achieving beneficial performance gains without channel state information (CSI). To elaborate a little further, the chaos sequence is embedded into the data-carrying matrices by a unique time-varying matrix. By employing differential coding during two adjacent signal blocks, a non-coherent detector can be developed without CSI knowledge. However, its theoretical performance analysis becomes challenging due to its complex construction. To address this issue, the theoretical average bit error probability (ABEP) lower and upper bounds of the TV-D-MIMO system are analyzed using the moment generating function (MGF) over generalized fading channel. The experimental results are shown that the derived ABEP upper and lower bounds are tight with the simulation results, which is helpful for future performance evaluation.