In this research, polydimethylsiloxane-polymethylmethacrylate (PDMS-PMMA) block copolymer was synthesized from polydimethylsiloxane (PDMS) and methylmethacrylate (MMA) monomer using atom transfer radical polymerization (ATRP). The synthesis characterization of the PDMS-b-PMMA copolymer membrane was carried out by a FT-IR, $^1H$-NMR, GPC and DSC. The permeabilities of nitrogen and hydrogen gases were observed being $1.2{sim}l.5$ barrer and $6.2{sim}10.5$ barrer, respectively. Simultaneously, selectivities of hydrogen against nitrogen were $5.3{sim}6.9$. The permeability and selectivity of PDMS-b-PMMA copolymer membrane were showed lower than the PDMS membrane, but higher than the PMMA membrane.