A diagnostic tool has been proposed to convert the observed surface distribution of hydrogen recombination line intensities into the radial distributions of the electron temperature and the density in HII regions. The observed line intensity is given by an integral of the volume emission coefficient along the line of sight, which comprises the Abel type integral equation for the volume emission coefficient. As the emission coefficient at a position is determined by the temperature and density of electrons at the position, the local emission coefficient resulted from the solution of the Abel equation gives the radial distribution of the temperature and the density. A test has been done on the feasibility of our diagnostic approach to probing of HII regions. From model calculations of an HII region of pure hydrogen, we have theoretically generated the observed surface brightness of hydrogen recombination line intensities and analyzed them by our diagnostic tool. The resulting temperatures and densities are then compared with the model values. For this case of uniform density, errors in the derived density are not large at all the positions. For the electron temperature, however, the largest errors appear at the central part of the HII region. The errors in the derived temperature decrease with the radial distance, and become negligible in the outer part of the model HII region.