In order to optimise the design of undulators using high-temperature superconductor (HTS) bulks we have developed a method to estimate the critical current density (Jc) of each bulk from the overall measured magnetic field of an undulator. The vertical magnetic field was measured along the electron-beam axis in a HTS bulk-based undulator consisting of twenty Gd-Ba-Cu-O (GdBCO) bulks inserted in a 12-T solenoid. The Jc values of the bulks were estimated by an inverse analysis approach in which the magnetic field was calculated by the forward simulation of the shielding currents in each HTS bulk with a given Jc. Subsequently the Jc values were iteratively updated using the pre-calculated response matrix of the undulator magnetic field to Jc. We demonstrate that it is possible to determine the Jc of each HTS bulk with sufficient accuracy for practical application within around 10 iterations. The pre-calculated response matrix, created in advance, enables the inverse analysis to be performed within a practically short time, on the order of several hours. The measurement error, which destroys the uniqueness of the solution, was investigated and the points to be noted for future magnetic field measurements were clarified. The results show that this inverse-analysis method allows the estimation of the Jc of each bulk comprising an HTS bulk undulator.