In order to improve the detection performance of ultra wideband (UWB) system, a nonlinear scaling UWB pulse based on generalized Gaussian pulse (GGP) was proposed in this paper. Then wideband ambiguity function (WBAF) of the pulse was derived and analyzed to show the relationship between its range ambiguity function and nonlinear scaling characteristic parameters. The simulation demonstrate that such UWB pulse can achieve the thumbtack WBAF, low side lobes and high range resolution can be achieved by increasing modulation frequency offset and decreasing modulation frequency. The simulation result can provide theoretic guidance to UWB pulse design.