Abstract: A method of designing constant modulus waveforms with ultra-low range sidelobe in specified intervals is presented. This kind of waveform can be used in radar, sonar, and communication systems with transmit adaptivity to suppress range sidelobe masking and multipath interferences. The 0-1 weighted integrated sidelobe level is used to construct the objective function, and the waveform design issue is modeled as a non-constrained optimization issue. According to the characteristics of the objective function, an initial waveform design algorithm based on power spectrum approximation is proposed. The analytical forms of objective function gradient and the Hessian matrix are derived and the subspace trust region algorithm is used, thus the computation burden of solving this optimization issue is reduced. Finally, the numerical simulations demonstrate that the proposed method can suppress successive and discrete intervals of range sidelobes effectively.