Hydrogen engine with homogeneous charged compression ignition can achieve high efficiency by high compression ratio and rapid chemical reaction rates spatially. However, it needs to expansion of the operation range with over-all load conditions which is very narrow due to extremely high pressure rise rate. The adoption of the lean boosting in a HCCI $H_2$ engine is expected to be effective in expansion of operation range since minimum compression ratio for spontaneous ignition is decreased by low temperature combustion and increased surround in-cylinder pressure. In order to grasp its possibility by using lean boosting in the HCCI $H_2$ engine, compression ratio required for spontaneous ignition, expansion degree of the operation range and over-all engine performance are experimentally analyzed with the boosting pressure and supply energy. As the results, it is found that minimum compression ratio for spontaneous ignition is down to the compression ratio(${varepsilon}$=19) of conventional diesel engine due to decreased self-ignition temperature, and operation range is extended to 170% in term of the equivalence ratio and 12 times in term of the supply energy than that of naturally aspirated type. Though indicated thermal efficiency is decreased by reduced compression ratio, it is over at least 46%.