We propose using sets of waveforms for different radar operation conditions based on wavelets. The new waveforms can adjust the bandwidth and transmission power adapting to the target and environmental conditions. Each scaling function or wavelet packet can form a narrow-bandwidth pulse with certain transmission power. Narrow bandwidth and large transmission power waveforms are effective for accurate speed detection of long-range targets. A new approach of pulse integration can summarize the detection results of multiple narrow bandwidth pulses producing a high range resolution result of an equivalently wide bandwidth pulse. For close-range tracking task, a set of wide bandwidth pulse waveforms (even a single waveform) with low transmission power can quickly update the range information, and reduce background interferences. The adaption approach is verified by experiments which also demonstrate the purposed waveforms suppressing range sidelobes more effectively than traditional linear frequency modulated (LFM) waveforms.