We report the results of an investigation on critical current measurements in bulk MgB2 superconductor by using Hall probe ac susceptibility. The temperature versus ac susceptibility has been measured as a function of external ac magnetic field with no dc part and magnitude in the range 240–1200 A/m by using the Hall probe method. The real part of the Hall probe susceptibility showed two-step transitions near critical temperature. We attributed this behavior to the anisotropic nature of the MgB2 compound. Close to the critical temperature the estimated anisotropy parameter is γ≈2.5, a value that is in fair agreement to the ones reported in the literature for polycrystalline and single crystals MgB2. We have also analyzed the susceptibility data within the framework of a critical state model (using the real part of the susceptibility) and an anisotropic nature of MgB2 compound. The inter-grain critical current is found to be 4×106 A/m2 at 39.59 K by using the critical state model. The temperature dependence of the critical current density was found to be in the form of Jc(T)∝(1−T/Tc)β, where β was calculated as 2.30 by using critical state model, respectively. Scanning electron microscopy was used for grain size estimation.