Abstract: Graphene is a cutting-edge research topic in condensed matter physics. This paper introduces the analytical solution of the pseudo-Landau energy level of graphene under a pseudo-magnetic field generated by the non-uniform uniaxial strain. We show in detail the derivation of the low-energy effective Hamiltonian under strain and the solution of related differential equations. The solution of the pseudo-Landau energy level, comprehensively using the basic knowledge of mathematics and physics learned by college students, is of great reference value for related  theoretical courses

Key words: graphene, inhomogeneous uniaxial strain, pseudo-magnetic field, pseudo-Landau level