Graphene has emerged as an attractive nonlinear-optical material due to the high coefficient of two-photon absorption and four-wave mixing. Four-wave mixing in graphene has been previously studied in silicon-photonic platform. Enhancement of the four-wave mixing using optical cavities such as silicon micro-ring resonator (MRR) has been demonstrated. Recently, similar experiments have been extended to silicon-nitride (SiN) waveguides and micro-ring resonators. Electrostatic tuning of the four-wave mixing, and generation of frequency combs have been demonstrated using SiN MRRs having a Q-factor of 106 at input pump powers ≥ 1 W. On-chip pump powers of the order of 10 mW to 100 mW are desirable to obtain high conversion efficiency of the four- wave mixing. However, such high on-chip powers are challenging to handle in integrated-optic platforms. We report preliminary experimental result of four-wave mixing in graphene-on-SiN MRRs with CW pump power of 120 μW, which is coupled to the MRR. The MRR used has a modest Q-factor of the order of 103 after transferring graphene. We observe four-wave mixing even with a 50 % coverage of monolayer graphene on the MRR. Such low power level allows low-power on-chip nonlinear process. Furthermore, low photon count could be used for quantum photonic process and fundamental research where high conversion efficiency may not be necessary.