We propose a direct-sequence pulse-amplitude modulation (DS-PAM) ultra-wideband (UWB) system which employs a non-linear chirp waveform instead of the conventional Gaussian monocycle in this paper. In the approved frequency for UWB, there exist myriad narrowband interferers. Specifically, we focus on the mutual interference between UWB systems and 802.11a WLAN. This paper offers a method to suppress this in-band narrowband interference by introducing a kind of non-linear chirp waveform. Using the proposed non-linear chirp waveform, the effects of one or more narrowband interference sources with different frequencies can be suppressed. System performance of UWB systems in the narrowband interference environment can be improved. Computer simulations with additive white Gaussian noise successfully demonstrate an increase in performance with the proposed system as compared to traditional linear chirp systems.