High-sensitivity plasmonic refractive index sensors show great applications in the areas of the biomedical diagnostics, healthcare, food safety, environmental monitoring, homeland security, and chemical reaction. However, the unstable and complicated environments considerably limit their practical applications. By employing the independent double Fano resonances in a simple metallic grating, we experimentally demonstrated a self-reference plasmonic sensor, which significantly reduces the error contributions of the light intensity fluctuations in the long-distance propagation and local temperature variations at the metallic grating, and the detection accuracy is guaranteed. The numerical simulation shows that the two Fano resonances have different originations and are independent with each other. As a result, the left Fano resonance is quite sensitive to the refractive index variations above the metal surface, while the right Fano resonance is insensitive to that. Experimentally, a high figure of merit (FOM) of 31 RIU-1 and FOM* of 860 RIU-1 are realized by using the left Fano resonance. More importantly, by using the right Fano resonance as a reference signal, the influence of the light intensity fluctuations and local temperature variations are monitored and eliminated in the experiment. This simple self-reference plasmonic sensor based on the double Fano resonances may find important applications in high-sensitive and accurate sensing under the unstable and complicated environments, as well as multi-parameter sensing.