To obtain high-purity hydrogen for industrial applications, it is highly desirable to separate and purify hydrogen from byproduct gases in hydrogen preparation. DFT calculations and MD simulations were performed to study the hydrogen separation performance of the graphenylene-like boron nitride (p-BN) monolayer under the modification of strain engineering. The p-BN membrane is thermal stable at high temperatures of 1500 K. Without strain engineering, the p-BN monolayer cannot be used as H-2 separation membranes at room temperature, as no H-2 gas can permeate from the membrane, however, it would be potential for H-2 separation at high temperatures (the H-2 permeance of 3.415 x 10(5)-2.732 x 10(6) GPU with high selectivity above 500 K). Strain engineering can effectively enhance the H-2 purification properties of the p-BN monolayer. At 9 % strains, the H-2 permeability of the p-BN membrane is 2.357 x 10(7) GPU at 300 K, much higher than the industrial acceptance value, while the selectivity of H-2 related to other gases (N-2, CO, O-2, CO2, and CH4) is 14.75, 33.09, 1.002 x 10(2), 8.512 x 10(5), and 1.502 x 10(10), respectively. Therefore, our findings indicate that the p-BN membranes are excellent candidates for highly controllable and reversible H-2 separation and purification under modification of strain engineering.