Alternans—an arrhythmic response of cardiac tissue to periodic pacing—often serves as a precursor to a more dangerous, and potentially lethal, state of fibrillation. Suppression of alternans using feedback control may be a plausible method to prevent fibrillation. Several approaches based on impulsive control have been proposed previously, where feedback is applied for a brief instance of time during each pacing interval. This paper presents a continuous-time approach, where feedback current is applied at all times, which is capable of suppressing alternans in fibers of significantly greater length (up to at least 4 cm), compared with impulsive control (less than 1 cm), and for a wide range of pacing cycle lengths.