We propose a double-layer graphene sheets side coupling to a strip of graphene to obtain the optical pulling or pushing force. Combined with coupled mode theory and finite-difference time-domain simulations, it is found that the conveyor belt effect can be realized in conjunction with the lateral optical equilibrium effect upon the radiation loss κe equal to the intrinsic loss κo. The maximum total optical force acting on the strip in the symmetric mode (S-mode) can be up to ∼5.95 in the unit of 1/c and the anti-symmetric (AS-mode) mode reach ∼2.75 1/c. The optical trapping potential Ux and optical trapping force Fx for the S-mode have a value around -22.5 kBT/W and 240 pN/W, while for the AS-mode can up to ∼-56 kBT/W and 520 pN/W, respectively. Our work opens a new avenue for optical manipulation with potential applications in optoelectronic devices and lab-on-a-chip platforms.