Intensity noise and its enhancement by external optical feedback in DFB lasers are investigated for the first time. Without external optical feedback, relative intensity noise of the DFB laser consistently decreases down to the detector noise limit as the injection current increases, because of the absence of mode hopping noise. The external feedback causes mode hopping among the external cavity modes or among the DFB modes. If the required threshold gain difference among the DFB modes is large, mode hopping among the DFB modes is suppressed; however, mode hopping remains among the external cavity modes. Mode hopping among the DFB modes and among the external cavity modes both cause a strong noise similar to hopping between laser modes in a FP laser. A numerical investigation shows that, even in the worst case, DFB lasers having a large coupling coefficient (KL≥2) endure more strongly against the external optical feedback when compared with conventional FP lasers having the same output facet reflectivity.