An optimal radar waveform-design method is proposed to detect moving targets in the presence of clutter and noise. The clutter is split into moving and static parts. Radar-moving target/clutter models are introduced and combined with Neyman–Pearson criteria to design optimal waveforms. Results show that optimal waveform for a moving target is different with that for a static target. The combination of simple-frequency signals could produce maximum detectability based on different noise-power spectrum density situations. Simulations show that our algorithm greatly improves signal-to-clutter plus noise ratio of radar system. Therefore, this algorithm may be preferable for moving target detection when prior information on clutter and noise is available.