In the favoured core-accretion model of formation of planetary systems, solid planetesimals accumulate to build up planetary cores, which then accrete nebular gas if they are sufficiently massive. Around M-dwarf stars (the most common stars in our Galaxy), this model favours the formation of Earth-mass (M % ) to Neptune-mass planets with orbital radii of 1 to 10 astronomical units (AU), which is consistent with the small number of gas giant planets known to orbit M-dwarf host stars 1-4 . More than 170 extrasolar planets have been discovered with a wide range of masses and orbital periods, but planets of Neptune's mass or less have not hitherto been detected at separations of more than 0.15 AU from normal stars. Here we report the discovery of a 5.5 15.5 22.7 M % planetary companion at a separation of 2.6 11.5 20.6 AU from a 0.22 10.21 20.11 M ( M-dwarf star, where M ( refers to a solar mass. (We propose to name it OGLE-2005-BLG-390Lb, indicating a planetary mass companion to the lens star of the microlensing event.) The mass is lower than that of GJ876d (ref. 5), although the error bars overlap. Our detection suggests that such cool, sub-Neptune-mass planets may be more common than gas giant planets, as predicted by the core accretion theory.Gravitational microlensing events can reveal extrasolar planets orbiting the foreground lens stars if the light curves are measured frequently enough to characterize planetary light curve deviations with features lasting a few hours 6-9 . Microlensing is most sensitive to planets in Earth-to-Jupiter-like orbits with semi-major axes in the range 1-5 AU. The sensitivity of the microlensing method to lowmass planets is restricted by the finite angular size of the source stars 10,11 , limiting detections to planets of a few M % for giant source stars, but allowing the detection of planets as small as 0.1M % for main-sequence source stars in the Galactic Bulge. The PLANET collaboration 12 maintains the high sampling rate required to detect low-mass planets while monitoring the most promising of the .500 microlensing events discovered annually by the OGLE collaboration, as well as events discovered by MOA. A decade of pioneering microlensing searches has resulted in the recent detections of two Jupiter-mass extrasolar planets 13,14 with orbital separations of a few AU by the combined observations of the OGLE, MOA, MicroFUN and PLANET collaborations. The absence of perturbations to stellar microlensing events can be used to constrain the presence of planetary lens companions. With large samples of events, upper LETTERS 1 PLANET/RoboNet Collaboration