We developed a laser system for the spectroscopy of the clock transition in ytterbium (Yb) atoms at 578 nm based on an interference-filter stabilized external-cavity diode laser (IFDL) emitting at 1156 nm. Owing to the improved frequency-to-current response of the laser-diode chip and the less sensitivity of the IFDL to mechanical perturbations, we succeeded in stabilizing the frequency to a high-finesse ultra-low-expansion glass cavity with a simple current feedback system. Using this laser system, we performed high-resolution clock spectroscopy of Yb and found that the linewidth of the stabilized laser was less than 320 Hz.