We report low frequency tunnel current noise characteristics of an organic monolayer tunnel junction. The measured devices, n-Si/alkyl chain (C18H37)/Al junctions, exhibit a clear 1/ f γ power spectrum noise with 1< γ <1.2. We observe a slight bias-dependent background of the normalized current noise power spectrum (SI/I²). However, a local increase is also observed over a certain bias range, mainly if V > 0.4 V, with an amplitude varying from device to device. We attribute this effect to an energy-dependent trap-induced tunnel current. We find that the background noise, SI, scales with . A model is proposed showing qualitative agreements with our experimental data.