Excitation of steep unidirectional broad-banded wave trains is studied numerically and experimentally. Iterative method is developed to adjust the driving signal of a paddle-type wavemaker to generate wave train with a prescribed free waves' spectrum. Analytical post-processing procedure based on the Zakharov equation is applied to separate complex amplitude spectrum of the surface elevation into free and bound components, as required for the proposed method of the adjustment of the wavemaker driving signal. Numerical wave tank in the simulations was based on application of the Boundary Element Method. The results of numerical simulations were supported by measurements in a wave tank. The measured and the designed shapes of the surface elevation variation with time, as well as of the corresponding amplitude spectra were found to be in a good agreement.