For the issue of deterioration in detection performance caused by dynamically changing environment in ultra-wideband(UWB) multiple input multiple output(MIMO) radar, this paper proposes a novel adaptive waveform design which is aimed to improve the ability of discriminating target and clutter from the radar scene. Firstly, a sequence of Morlet wavelet pulses with frequency hopping and pulse position modulation by Welch-Costas array is designed. Then a waveform optimization solution is proposed which is achieved by applying the minimization mutual-information(MI) strategy. After that, with subsequent iterations of the algorithm, simulation results demonstrate that the optimal waveform design method brings an improvement in the target detection ability in the presence of noise and clutter. For the issue of deterioration in detection performance caused by dynamically changing environment in ultra-wideband (UWB) multiple input multiple output (MIMO) radar, this paper proposes a novel adaptive waveform design which is aimed at improving the ability of discriminating target and clutter from First, a sequence of Morlet wavelet pulses with frequency hopping and pulse position modulation by Welch-Costas array is designed. Then a waveform optimization solution is proposed which is achieved by applying the minimization mutual-information (MI) strategy. After that with subsequent iterations of the algorithm, simulation results demonstrate that the optimal waveform design method brings an improvement in the target detection ability in the presence of noise and clutter.