We propose a narrow-spectral-linewidth silicon photonic wavelength-tunable laser with a novel external wavelength-tunable filter, which consists of two silicon ring resonators with different circumferences and a highly asymmetric Mach-Zehnder interferometer (MZI), the two optical paths of which have significantly different lengths. Calculations and experimental results indicated that the gain difference between longitudinal modes was increased by the highly asymmetric MZI. Consequently, a narrow spectral linewidth of 12 kHz and a stable single-mode oscillation were obtained.