Pulse waveform design problems of cognitive ultra wide band (CUWB) are studied, and a method of optimized combination Morlet wavelet is proposed. On the basis of characteristic analysis in time and frequency domain of Morlet, the design steps of the method are worked out. Firstly, the value area of wavelet stretching factor is acquired by the use of dichotomy method under the action of power spectrum density (PSD) met the needs of FCC spectral mask. Then, optimized weight is searched by designing programmable logistic language so as to get combined UWB pulse with high frequency spectrum efficiency. In consideration of authorized frequency band detected by cognitive user, band-stop filter is designed for suppressing narrow band interference, thus CUWB pulse waveform is got by making UWB pulse pass the designed filter. The simulation shows that the proposed method is susceptible to realization and operation, the designed waveform has good autocorrelation character and high spectrum utilization ratio, which provides a new thought for waveform design of CUWB.