We present the results of the INTEGRAL monitoring campaign on the accreting low mass X-ray binary pulsar GX 1+4 performed during the Galactic plane scan of the INTEGRAL Core Programme . The source was observed in different luminosity states ranging from L _ { 20 - 40 \mathrm { keV } } = 1.7 \times 10 ^ { -10 } \mathrm { erg cm ^ { -2 } s ^ { -1 } } , to L _ { 20 - 40 \mathrm { keV } } = 10.5 \times 10 ^ { -10 } \mathrm { erg cm ^ { -2 } s ^ { -1 } } for about 779 ks from March 2003 until October 2004 . Our observations confirm the secular spin down of GX 1+4 with the spin period ( P _ { \mathrm { s } } ) varying from 139.63 s to 141.56 s. In the highest luminosity state , a spin-up phase is observed . The phase-averaged spectrum of the source was modelled either with an absorbed cut-off power law or with a Comptonization model with significantly different parameters in the two brightest luminosity states . No evidence of any absorption-like feature is observed in the phase averaged spectrum up to 110 keV . At highest luminosity , the source is found to pulsate up to 130 keV . Phase resolved spectroscopy reveals a phase-dependent continuum and marginal evidence for an absorption feature at 34 \pm 2 keV in the descending part of the pulse . If interpreted as due to electron resonant cyclotron scattering , the magnetic field in the emitting region would be ( 2.9 \pm 0.2 ) \times 10 ^ { 12 } ( 1 + z ) G where z is the gravitational red shift of the emitting region . We also observed a very low luminosity state , typical of this source , which lasted for about two days during which the source spectrum was modelled by a simple power law , and a pulsed signal was still detectable in the 15–100 keV energy range .