Noble metals (Au and Ag) are the primary raw materials which have vast potential application ranging from across biosensor, biomedicine, science, and engineering fundamental. However, alloying them will enhance the efficiency and applicability of noble metals. Employing the linear-weight (LW) technique to construct a dielectric function of a binary solution is still disputed. However, this method is still widely used to examine Localized Surface Plasmon Resonance (LSPR) of Au-Ag binary solution. In this work, the calculation of electromagnetic response such as Localized Surface Plasmon Resonance (LSPR) of bimetallic Au-Ag nanorod was performed by means of MNPBEM package. We utilized nanorod-shaped with two different excitation modes, namely, Transverse Mode (TM) and Longitudinal Mode (LM), and various compositions to investigate their LSPR shifting anomalies. Moreover, we employed the LW technique to construct their dielectric function and analyze the LSPR anomalies. Interestingly, we found that using LW approximation, the resonance peak of TM is separate into two peaks. These peaks originated from the free electron of Au and Ag respectively, however, some of LSPRs peak did not occur amongst peak of pure Au and Ag. Practically, using LW method the resonance peak should be located amongst their individual elements. This work has provided the limitation of using silver fraction and the related aspect ratios to predict the LSPR spectra of Au and Ag on nanorod-shaped.