An angular analysis of the decay J/psi ->mu (+) mu (-) is performed to measure the polarization of prompt J/psi mesons produced in pp collisions at . The dataset corresponds to an integrated luminosity of 0.37 fb(-1) collected with the LHCb detector. The measurement is presented as a function of transverse momentum, p (T), and rapidity, y, of the J/psi meson, in the kinematic region 2 < p (T)< 15 GeV/c and 2.0 < y < 4.5.