An analytical approach that can rapidly determine a wide range of hydrogen concentration in solid-state materials has been recently demanded to contribute to the hydrogen economy. This study presents a method for estimating hydrogen concentrations ranging from 0.2 to 7.6 mass % via laser-induced breakdown spectroscopy (LIBS) in a few seconds, with an improvement in the upper limit of determination (7.6 mass %) by approximately 1.3 times compared with a previous work (5.7 mass %). This extension of the determinable concentration range was achieved by measuring the emission intensity at 656.28 nm from the sample in a helium atmosphere at 3000 Pa under focused laser irradiation and by reducing the water residues in both the sample and gas line of the LIBS system. The as-determined hydrogen concentrations in magnesium hydride (MgH2) samples agreed well with those estimated through inert gas fusion/gas chromatography. The calibration curve for LIBS analysis was acquired by measuring the emission intensity at 656.28 nm of standard Mg/MgH2 mixtures containing various hydrogen concentrations (0, 0.1, 0.2, 0.5, 1.0, 2.0, 3.0, 4.0, 5.0, and 7.6 mass %). Results indicated that the proposed LIBS-based method is applicable to the rapid quantitative analysis of hydrogen in hydrogen-containing material of MgH2.