Focusing on the issue that the Signal-to-Clutter-and-Noise Ratio (SCNR) of echo signal is low when cognitive radar detects extended target, a waveform design method based on SCNR was proposed. Firstly, the relation between the SCNR of cognitive radar echo signal and the Energy Spectral Density (ESD) of transmitted signal, was gotten by establishing extended target detection model other than previous point target model; secondly, according to the maximum SCNR criterion, the global optimal solution of the transmitted signal ESD was deduced; finally, in order to get a meaningful time-domain signal, ESD was synthesized to be a constant amplitude based on phase-modulation after combining with the Minimum Mean-Square Error (MMSE) and iterative algorithm, which met the emission requirements of radar. In the simulation, the amplitude of time-domain synthesized signal is uniform, and its SCNR at the output of the matched filter is 19.133 dB, only 0.005 dB less than the ideal value. The results show that not only can the time-domain waveform meet the requirement of constant amplitude, but also the SCNR obtained at receiver output can achieve the best approximation to the ideal value, and it improves the performance of the extended target detection.