The fuel rod instability can be occurred because of the axial and cross flow due to the flow anomaly and/or flow redistribution in the lower core plate region of the pressurized water reactor. The fuel rod vibration due to the hydraulic instability is one of the root causes of fuel failure. The verification on the fuel rod vibration and instability is needed for the new fuel assembly design to verify the fuel rod instability. In this study, the fuel rod vibration and stability analyses were performed to investigate the effect of the grid height, fuel rod support condition, and span adjustment on the fuel rod vibration characteristics for the advanced $16{ imes}16$ fuel assembly design. Based on the analysis results, the grid height and grid axial elevation of the advanced $16{ imes}16$ fuel assembly design were proposed.