This paper presents a novel method of enhancing esophageal speech using statistical voice conversion. Esophageal speech is one of the alternative speaking methods for laryngectomees. Although it doesn't require any external devices, generated voices usually sound unnatural compared with normal speech. To improve the intelligibility and naturalness of esophageal speech, we propose a voice conversion method from esophageal speech into normal speech. A spectral parameter and excitation parameters of target normal speech are separately estimated from a spectral parameter of the esophageal speech based on Gaussian mixture models. The experimental results demonstrate that the proposed method yields significant improvements in intelligibility and naturalness. We also apply one-to-many eigenvoice conversion to esophageal speech enhancement to make it possible to flexibly control the voice quality of enhanced speech.