An economic hydrogenation process is provided which significantly suppresses palladium catalyzer activity loss, for obtaining very high purity 1,4-CHDA through a simple operation. The process includes bringing the solution containing the hydrogenation reaction product of interest into contact with steam. The resultant products may include resins having excellent weather resistance or physical properties or high purity medical drugs. The process for preparing 1,4-cyclohexandicarboxylic acid is characterized by two consecutive steps. The first step includes the hydrogenation of a solution containing terephthalic acid in the presence of a palladium catalyzer in an acid resistant vessel or in a vessel layered with acid resistant material for preparing 1,4-cyclohexandicarboxylic acid. The second step includes contacting the solution containing 1,4-cyclohexandicarboxylic acid obtained in the first step with the steam, and extracting impurities moved to the steam.