The LLP variational method with linear combination operator are used to study the properties of weak coupling polarons in monolayer graphene(MG). The relationships between the ground state energy of weak coupling polarons, Debye wavenumber of the phonon and the vibrational frequency have been investigated. It is found that the first excited state energy and transition energy(TE) of the polaron has a linear relationship with the Debye cut-off wavenumber(DW), and the vibrational frequency. The result of numerical calculation shows that the ground state energy, the first excited state energy and TE of the polaron in MG can be tunabled by controlling the DW and vibrational frequency. The ground state energy increases with the increase of DW and vibrational frequency, while the first excited state energy and transition energy are not monotone function of vibrational frequency.