Passive source location is a fundamental problem in earthquake seismology and reservoir characterization with fluid injection. It has been shown that Geometric-mean Reverse-Time Migration (GmRTM) can produce source images with improved resolution and fewer migration artifacts than conventional time-reversal imaging in acoustic media. However, the acoustic assumption often requires data windowing and polarity correction when we apply it to the elastic data, which involves manual efforts and introduces uncertainties. Therefore, we extend this cross-correlation-based GmRTM imaging method to elastic media. Back-propagation and Helmholtz decomposition are conducted individually for each receiver wavefield, after which we apply zero-lag cross-correlations over the decoupled P- or/and S- wavefields to obtain the corresponding P-, S- and PS-source images. Considering the influences of random noise, anisotropy and interferences from multiple sources, we test the proposed elastic GmRTM method on a synthetic example with layered model and demonstrate its advantages over other imaging conditions (e.g., time-reversal imaging). The method is further validated using another synthetic test based on the elastic Marmousi model and a field-data example from Oklahoma.