There are many obstacles to applying waveform inversion to seismic data. However, the most critical factor is the absence of the low-frequency components that are needed for constructing long-wavelength structure. This problem stems from the highly nonlinear property of waveform inversion, which causes the algorithm to be trapped in a local minimum. The waveform inversion in the Laplace domain, rather than the usual frequency domain, is capable of producing velocity models with long-wavelength information. A study on this method was recently published, which was limited to the problem of acoustic media. In this paper, we extend Laplace-domain waveform inversion to elastic media. Unlike acoustic inversion, elastic inversion requires sophisticated manipulation of the gradient direction. We suggest a method to modify pseudo-Hessian matrices by using a heuristic weighting function. We test our inversion algorithm on synthetic seismic data generated using the Society of Exploration Geophysicists/European Association of Geoscientists & Engineers (SEG/EAGE) salt-dome model and the Commission on Controlled-Source Seismology (CCSS) model. Inversion results using these data sets also produce the long-wavelength velocity model and demonstrate that Laplace-domain waveform inversion is robust to the initial velocity model. Furthermore, we provide an example showing that our inverted result is a suitable initial model for the frequency-domain waveform inversion.