Acoustomagnetoelectric Effect (AME) in Graphene Nanoribbon (GNR) in the presence of an external electric and magnetic fields was studied using the Boltzmann kinetic equation. On open circuit, the Surface Acoustomagnetoelectric field (ESAME) in GNR was obtained in the region ql >> 1, for energy dispersion "(p) near the Fermi level. The dependence of ESAME on the dimensional factor (ɳ), the sub-band index (pi), and the width (N) of GNR were analyzed numerically. For ESAME versus ɳ, a non-linear graph was obtained. From the graph, at ɳ < 0.62, the obtained graph qualitatively agreed with that experimentally observed in graphite. However at ɳ > 0.62, the ⃗ESAME falls rapidly to a minimum value. We observed that in GNR, the maximum ⃗ESAME was obtained at magnetic field H = 3.2Am−1. The graphs obtainedwere modulated by varying the subband index pi with an inversion observed when pi = 6. The dependence of ESAME on the width N for various pi was also studied where, ⃗ESAME decreases for increase in pi. To enhanced the understanding of ESAME on the N and ɳ, a 3D graph was plotted. This study is relevant for investigating the properties of GNR.