Using the first-principles density functional method, the stability characteristics, mechanical and vibrational properties of two-dimensional boron-substituted ThMoB4-type graphene configurations (BSCs) were systematically investigated to design new geometries with various advantages coming from boron. The cohesive energies were calculated at first to confirm the energetic stability of the structures. The single-crystal elastic constants were evaluated to explore their mechanical stabilities and the relevant mechanical properties such as layer modulus, Young's modulus, and Poisson ratio. Phonon dispersions were studied to examine the dynamic stability of the structures. It is noticed that ThMoB4-type graphene (ThMoB4-C) is more energetically stable than the boron-included configurations. All the boron-substituted allotropes are mechanically stable, and ThMoB4-C has the highest mechanical properties. The calculated mechanical properties were compared to those of other 2D graphene allotropes. It can be expected from the complete stability analysis that it is possible to synthesize some of these boron-substituted configurations. Notably, they can be used in hydrogen storage and battery applications.