State-of-the-art research on narrow-linewidth external cavity semiconductor lasers has provided limited discussion on the capability of continuous wavelength tuning. In this study, we present a 780 nm tunable external cavity diode laser (ECDL) with narrow linewidth. An angle-adjustable interference filter (IF) is employed as the mode-selection element, enabling a wide wavelength tuning range. Precise, mode-hop-free continuous tuning is achieved through a combination of current modulation and piezoelectric ceramic transducer (PZT) control, with a tuning accuracy of 1.65 pm/mA. Experimental optimization of the interference filter external cavity diode laser (IF-ECDL) operating conditions resulted in a narrow linewidth of 55 kHz and a high output power of 51 mW. Furthermore, by integrating current and PZT tuning, continuous wavelength tuning of the IF-ECDL output is demonstrated over a specified range.