A new method for designing single/multiple unimodular waveforms with good weighted correlation properties, which is
based on minimizing the weighted integrated sidelobe levels of waveforms, is developed. The main contributions of the paper lie in formulating the objective as a quartic form where Hadamard product of matrices is involved, converting the nonconvex quartic optimization problem into a quadratic form and then solving it by means of majorization-minimization technique which seeks to find the solution iteratively. Corresponding algorithm enables good weighted correlations of the designed waveforms and shows fast convergence compared with existing methods.