Elastic least-squares reverse time migration (LSRTM) has been developed recently for its high accuracy imaging ability. The theory is based on minimizing the misfit between the observed and simulated data by an iterative algorithm to refine seismic images toward the true reflectivity. We have developed a new elastic LSRTM with the same modeling equations for source and receiver wavefield extrapolations, except for their source terms. The LSRTM has a natural advantage to solve the source and receiver wavefields using the same modeling system; thus, it is easy to implement LSRTM. In practice, it is difficult to obtain an accurate source wavelet, so a convolution-based objective function is used in our source-independent elastic LSRTM. Such an objective function can relax the requirement of an accurate wavelet, and improve the robustness of the inverse problem in the presence of noise. The numerical examples indicate that our method has the ability to recover the reflectivity models with an incorrect source wavelet from noisy data.