The invention discloses SBS containing a 1,2 structure uniformly distributed butadiene block and a hydride thereof and a preparation and application method thereof. According to the preparation process of the SBS, styrene reacts with an initiator under the action of an activator to initiate first-stage polymerization. During the second-stage polymerization process, a 1,2 structure regulator is dissolved in butadiene and the solution is uniformly added to a polymerization kettle within 16 to 18 minutes, and the reaction is further carried out for 8-12 min after the addition. During the third-stage polymerization, styrene can be used for the polymerization or a coupling agent can be adopted for coupling, the content of the 1,2-addition unit in the polybutadiene segment of the SBS is 38-42% and the 1,2-addition unit is uniformly distributed. SEBS obtained after hydrogenation has good compatible stability with naphthenic oil or white oil, and the oil has low mobility in SEBS and high lighttransmittance, and can be widely applied to transparent elastic materials.