The structural stability, electronic and magnetic properties of semihydrogenated graphene and monolayer boron nitride (H-Gra@BN) composite system are studied by the first principles calculation. First, for the six possible stacked configurations of H-Gra@BN in three kinds of magnetic coupling manners, including the nonmagnetic, ferromagnetic and antiferromagnetic, the geometry optimization structures are calculated. The formation energies (Ef) are -28, -37, -40, -35, -28, and -34 meV/atom for AA-B, AA-N, AB-B, AB-B-H, AB-N and AB-N-H configurations of H-Gra@BN, respectively. The details of the six H-Gra@BN configurations are presented. The results show that the AB-B configuration of H-Gra@BN system is most stable with the largest formation energy in the six configurations. Its thickness is the smallest in all six configurations. The formation energies of all configurations are very close to each other and show that the combination of the interlayer between layers is very weak, The interaction between H-Gra and monolayer BN is van der Waals binding. Second, the band structure, total density of states (TDOS), partial density of states and polarization charge density of the most stable H-Gra@BN system are systematically analyzed. This material is ferromagnetic semiconductor. The band gaps for majority and minority spin electrons are 3.097 eV and 1.798 eV, respectively. Each physical cell has an about 1 μB magnetic moment, which is mainly derived from the contribution of the unhydrogenated C2 atom. Furthermore, while the pressure is applied along the z direction, we analyze the TDOS and band structure of H-Gra@BN system, and find that when the z axis strain is more than -10.48% (Δh=-0.45 Å), the valence band maximum of minority spin moves down. The conduction band minimum of minority spin moves from the high symmetry Γ position into a position between Γ and K. The electronic properties of the most stable H-Gra@BN system change from magnetic semiconductor into half metal. When the strain is increased by more than -11.65% (Δh=-0.5 Å), the most stable H-Gra@BN changes into a nonmagnetic metal. To analyze the effect caused by different strains, we analyze the difference in three-dimensional charge density, and find that with the decrease of the layer spacing, the interlayer interaction gradually increases and shows the obvious covalent bond characteristics. This paper predicts a new type of two-dimensional material of which the electronic and magnetic properties can be easily tuned by pressure, and it is expected to be used in nano-devices and serve as an intelligent building material.