The bursting pulsar, GRO J1744-28, went again in outburst after ∼18 years of quiescence in mid-January 2014. We studied the broad-band, persistent, X-ray spectrum using X-ray data from a XMM-Newton observation, performed almost at the peak of the outburst, and from a close INTEGRAL observation, performed 3 days later, thus covering the 1.3-70.0 keV band. The spectrum shows a complex continuum shape that cannot be modelled with standard high-mass X-ray pulsar models, nor by twocomponents models. We observe broadband and peaked residuals from 4 to 15 keV, and we propose a self-consistent interpretation of these residuals, assuming they are produced by cyclotron absorption features and by a moderately smeared, highly ionized, reflection component. We identify the cyclotron fundamental at ∼ 4.7 keV, with hints for two possible harmonics at ∼ 10.4 keV and ∼ 15.8 keV. The position of the cyclotron fundamental allows an estimate for the pulsar magnetic field of (5.27 ± 0.06) × 10 11 G, if the feature is produced at its surface. From the dynamical and relativistic smearing of the disk reflected component, we obtain a lower limit estimate for the truncated accretion disk inner radius, ( 100 R g ), and for the inclination angle (18• -48 • ). We also detect the presence of a softer thermal component, that we associate with the emission from an accretion disk truncated at a distance from the pulsar of 50-115 R g . From these estimates, we derive the magneto-spheric radius for disk accretion to be ∼ 0.2 times the classical Alfvén radius for radial accretion.