Abstract We report on the intrinsic magnetic properties of a GdCo 4 B single crystal as derived from magnetization measurements. The occurrence of a first-order magnetization process (FOMP) in a magnetic field applied perpendicularly to the easy magnetization direction provides an opportunity to determine the anisotropy parameters K 1 and K 2 . To this end, the theoretical approach proposed previously for easy-plane magnets has been adapted for the case of easy-axis compounds exhibiting a FOMP. The obtained anisotropy parameters of GdCo 4 B are compared with the values deduced by other classical techniques. The presence of a compensation point in the thermal dependence of the spontaneous magnetization has enabled the determination of the exchange field on Gd, B ex = 131 T, which is in good agreement with inelastic neutron scattering results published earlier. Influence of the applied pressure on the anisotropy parameters is quantified using the pressure dependence of the FOMP, revealing a significant sensitivity of the anisotropy parameters to pressure.