Stellar winds of cool main-sequence stars are difficult to constrain observationally. One way to measure stellar mass-loss rates is to detect the soft X-ray emission from stellar astrospheres produced by charge exchange between heavy ions of the stellar wind and cold neutrals of the interstellar medium surrounding the stars. Here we report detections of charge-exchange-induced X-ray emission from the extended astrospheres of three main-sequence stars, 70 Ophiuchi, ϵ Eridani and 61 Cygni, based on the analysis of XMM-Newton observations. We estimate the corresponding mass-loss rates to be 66.5 ± 11.1, 15.6 ± 4.4 and 9.6 ± 4.1 times the solar mass-loss rate for 70 Ophiuchi, ϵ Eridani and 61 Cygni, respectively, and compare our results with the alternative ’hydrogen wall’ method. We also place upper limits on the mass-loss rates of several other main-sequence stars. This method has potential utility for determining the mass-loss rates from X-ray observations showing spatial extension beyond a coronal point source.