Ambient noise seismic tomography has proven to be an effective tool for subsurface imaging, particularly in volcanic regions such as the Reykjanes Peninsula (RP), SW Iceland, where ambient seismic noise is ideal with isotropic illumination. The primary purpose of this study is to obtain a reliable shear wave velocity model of the RP, to get a better understanding of the subsurface structure of the RP and how it relates to other geoscientific results. This is the first tomographic model of the RP which is based on both on- and off-shore seismic stations. We use the ambient seismic noise data and apply a novel algorithm called one-step 3-D transdimensional tomography. The main geological structures in the study area (i.e. covered by seismic stations) are the four NE-SW trending volcanic systems, orientated highly oblique to the plate spreading on the RP. These are from west to east; Reykjanes, Eldvörp-Svartsengi, Fagradalsfjall and Krýsuvík, of which all except Fagradalsfjall host a known high-temperature geothermal field. Using surface waves retrieved from ambient noise recordings, we recovered a 3-D model of shear wave velocity. We observe low-velocity anomalies below these known high-temperature fields. The observed low-velocity anomalies below Reykjanes and Eldvörp-Svartsengi are significant but relatively small. The low-velocity anomaly observed below Krýsuvík is both larger and stronger, oriented near-perpendicular to the volcanic system, and coinciding well with a previously found low-resistivity anomaly. A low-velocity anomaly in the depth range of 5-8 km extends horizontally along the whole RP, but below the high-temperature fields, the onset of the velocity decrease is shallower, at around 3 km depth. This is in good agreement with the brittle-ductile transition zone on the RP. In considerably greater detail, our results confirm previous tomographic models obtained in the area. This study demonstrates the potential of the entirely data-driven, one-step 3-D transdimensional ambient noise tomography as a routine tomography tool and a complementary seismological tool for geothermal exploration, providing an enhanced understanding of the upper crustal structure of the RP.@en