An narrow-linewidth external-cavity diode laser (ECDL) is presented based on a parallel monolithic folded Fabry-Perot (F-P) cavity. The frequency of the laser is locked to the monolithic F-P resonance by optical feedback. Linewidth of the laser is measured with delayed self-heterodyne method. Experimental results show the linewidth of ECDL is narrower than 35 kHz. Linewidth of ECDL changes when the position of coupling on the input/output plane changes.