Full-waveform inversion (FWI) is a highly non-linear optimization problem which aims at retrieving high-resolution models of the subsurface parameters. Elastic FWI (EFWI) should provide a better representation to the elastic nature of the subsurface than the simple acoustic assumption. However, including elastic parameters in the EFWI requires higher the computational cost and storage memory not to mention the added complexity of dealing with multi parameters and higher nonlinearity in the inversion. To mitigate these problems, we propose an efficient wavefield inversion (EWI) for elastic media. By inverting for a background model wavefield that partially fits the data and the wave equation for a modified source, we are able to extend the search space at a reduced cost. It also saves the storage memory by avoiding storing the background wavefields. We formulate the P- and S-wave velocity perturbations into a linear inversion system to reduce the tradeoff in the multi-parameter waveform inversion. Applications on synthetic data generated from a modified Overthrust model and a modified Marmousi model show the effectiveness of the proposed method.