The Acoustomagnetoelectric Effect (AME) in Graphene Nanoribbon (GNR) was theoretically studied using the Boltzmann kinetic equation. On open circuit, the general formular for Surface Acoustomagnetoelectric field (\(\vec{E}_{SAME}\)) in GNR with energy dispersion \(\varepsilon(p)\) near the Fermi point was calculated. The \(E_{SAME}\) was found to depend on the magnetic strength (\(\eta\)), \(\alpha\) = \({\hbar \omega_q}/{E_g}\) and the energy gap (\(E_g\)). The expression for \(\vec{E}_{SAME}\) was analyzed numerically for varying width of GNR, magnetic strength (\(\eta\)) and \(\alpha\) at different sub-bands indices (\(p_i\)). It was noted that the dependence of \(\vec{E}_{SAME}\) on the width of GNR increased to a saturation point of approximately \(15\)Vcm\(^{-1}\) and remained constant. For \(E_{SAME}\) versus \(\eta\), the \(E_{SAME}\) increases rapidly to a maximum point and then decayed to a constant minimum value. The graph was modulated either by varying the width of GNR or the sub-band index \(p_i\) with an inversion occurring at \(p_i = 6\). The dependence of \(E_{SAME}\) versus \(\alpha\) was analyzed. The \(E_{SAME}\) was constant up to a point and sharply increased asymptotically at approximately \(\alpha = 1\). A \(3\)D graph of \(\vec{E}_{SAME}\) with \(\eta\) and width is also presented. This study is relevant for investigating the properties of GNR.